Prior to each preparation, wash winter squash and pumpkins with warm water and a very small amount of mild soap. Rinse well and dry with a kitchen towel.
Cutting winter squash is treacherous whether the shell is thick or thin. Work on a solid cutting board with a non-skid footing*; position the board so that you will have a comfortable angle when addressing the squash with your knife. Your first goal is to remove the stem, your second is to halve the squash evenly.
Place the cleaned squash on your board, stem end up. Use a sharp, sturdy chef's knife to pierce the shell near the stem. With force and caution, work the blade into the flesh; remove blade. Rotate the squash about 30 degrees before repeating process. It should take about six repetitions to cut out stem. Set your blade aside before removing stem. It may be necessary to use a sturdy offset spatula or other non-sharp tool to leverage the stem out. The ease with which the stem is removed will be different in each variety, but this step is generally not problematic.
Again, piece the shell at or near the stem hole you've just created. With force and caution, work the blade into the flesh. Taking care to not tip the squash, cut an even line towards the blossom end. Remove blade before turning the squash 180 degrees. Repeat process to cut another line opposite the first. Remove blade before flipping squash so that the blossom end is facing up. Cut to continue lines to their nexus; they should come close to lining up. Set your blade aside before pulling apart the hemispheres of the squash.
Set one half aside while working on the other. Place the hemisphere cut side down on board. Using the same method of caution and force, halve. To break down into eighths, repeat process, this time with skin side on board.
Preheat oven to 400ºF
Halve sqash from stem to blossom. Divide each segment into halves. With a metal or sharp-edged plastic scoop/spoon, scoop stringy pulp and seeds from cavity, reserve in a large bowl. Cut each quarter into halves, keeping pieces as equal as possible.
Lightly oil exposed flesh with vegetable oil or vegetable oil-olive oil blend. Arrange pieces, skin side down, on a half-sheet pan.
Cook for 40-60 minutes, as determined by the variety of squash you are preparing.
Place a steamer insert into a 4 or 6 quart pressure cooker. Pour 1 cup of water into the bottom of the cooker.
Wash and quarter pumpkin and chop into roughly 1.5-inch pieces. Peeling is optional; some squash are easier to peel before cooking, others after.
Arrange pieces as evenly as possible in cooker, not filling the cavity above 2/3 full. Lock lid closed. Over high heat, bring to cooker to high pressure. Maintain high pressure for 3-4 minutes, adjusting burner as necessary.
Quick-release pressure by running water over the closed cooker. Remove lid and test squash - if the flesh is not fork tender, replace lid and lock in place; allow squash to continue to cook in residual heat for another 4-6 minutes.
Remove pieces from cooker and let cool slightly before removing skin and consuming or puréeing.
Wash, break down and roast winter squash. Once squash segments are cool enough to handle, use a large spoon to scoop flesh from skin. Place in the bowl of a food processor or carafe of blender. Process on medium-high speed for several minutes, until even and smooth; it may be necessary to add water to ease the textural transition.
If the flesh is exceptionally stringy, or to achieve a totally smooth texture, pass purée through a sieve before using or storing.
Pour into resealable bags or containers to freeze.
Place seeds and scooped strings/pulp in a large bowl. Fill partway with water. Press seeds from pulp and discard pulp. Occasionally, stir water briskly to ease this separation. Once the ratio of pulp to seeds is tipped in the favor of the latter, drain bowl through a pasta colander. Scoop seeds back into large bowl and refill partway with water. Repeat squeezing, stirring, drainging until there are very few strings remaining. Drain seeds and spread out on towel-lined sheet pan. Let air dry for 2 hours, sometimes manipulating towel to separate and redistribute seeds.
Preheat oven to 350ºF. Spread dried seeds in an even layer in a rimmed half-sheet pan. Toast, stirring somewhat frequently, until shells are golden-brown and fragrant. Remove sheet from oven. If you so desire, toss hot seeds with kosher salt and a small amount of vegetable oil. Let cool before consuming.