This half-baked (or perhaps, half-boiled?) idea is pretty much Exactly What It Says On The Tin. First, extract juice from a pumpkin, then remove water from the juice until it's viscosity is similar to maple syrup. That's it! :)
Probable uses of this imagined ingredient could be many: in mixed drinks, in cakes or pies, on or in ice cream... anywhere you might use a flavored syrup, you could use pumpkin reduction.
Ok, for a bit more elaboration: there are a few different ways of getting juice from a pumpkin, some of which don't even involve buying / growing any more of our main ingredient than we otherwise would.
First, start by doing preparations for making pumpkin pie from fresh pumpkin... However many pie than you would normally cook around the Thanksgiving / Christmas season, but you must have a recipe which uses fresh pumpkin, not canned.
The first step in most pumpkin pie recipes is to remove and discard the guts of the pumpkin. For making pumpkin reduction, take the pumpkin guts out of the pumpkin, cook them slightly (to increase juice extraction), then put them into a vegetable juice extractor; discard the solids, and put the liquid in a pot on the stove, and start reducing that liquid down to a syrup.
The second step of pumpkin pie making is generally to cut up the pumpkin flesh, then bake it. For this idea, make sure that the pumpkin chunks are on a wire rack, raised high enough above a roasting pan that, while cooking, they won't sit in the juice which comes out. After baking, pour this liquid into the pot, stirring it into the (slightly reduced) pumpkin gut juice.
Third, take a small portion of the baked pumpkin flesh, and run it through the juice extractor. Stir the liquid into the pot, and put the solids with the rest of the baked pumpkin. This will result in a slightly dryer pumpkin pie, which IMHO is a good thing (I've seen many pumpkin pies which have a puddle of liquid on top, which is rather unappealing). If you think the pie will be too dry, replace some or all of the removed liquid with apple juice or cider.
Finish making the pumpkin pie, and continue cooking the liquid until it reaches the right viscosity.
Note that there is only *one* ingredient in this pumpkin reduction: pumpkin (juice)!
Obviously if you really want to, you could add some pumpkin pie spice to it, but be careful not to add too much, or the flavor might overpower the pumpkin.-- goldbb, Nov 30 2012 Before I forget... if you've grown a pumpkin which you don't plan on eating (e.g., a large, decorative Jack O Lantern, or a giant pumpkin, both of which have coarse, stringy textures), you can of course make juice (or syrup) out of it!
Cook and juice the pumpkin guts, cook the flesh and use the drippings, then juice all of the cooked pumpkin flesh, discarding the solids.
Since both jack-o-lanterns and giant pumpkins are said to have "watery" flesh, I would expect that the juice will be watery, and thus take longer to cook down to syrupy goodness.
PS: No, I haven't forgotten the seeds! It is your choice whether to leave them in, or remove them. The taste will probably change, depending on their presence, but it'll probably be good either way.-- goldbb, Nov 30 2012 Of COURSE you remove them. That way you can roast and eat them.
I used to oven roast them with oil and salt, but it's difficult to monitor the degree of roastiness and the failure mode is burning.
Now I pan toast them dry, then add butter and salt at the final stage.-- normzone, Nov 30 2012 random, halfbakery