Make filling: Preheat oven to 425º. Put squash chunks in a rimmed baking pan, drizzle with olive oil, and season generously with salt and pepper. Toss to coat. Bake, stirring squash every 20 minutes, until very tender, 35 to 45 minutes. Carefully spoon hot squash into a food processor and whirl until very smooth.
Scrape squash into a large bowl and let cool. Stir in almonds, sage, parmesan, and nutmeg. Add salt and pepper to taste.
Assemble ravioli: Line a rimmed baking pan with parchment paper and sprinkle with semolina; set aside. Lay 1 pasta sheet on a work surface. Starting 2 in. away from a short end, spoon a 2-tbsp. mound of filling onto the middle of pasta sheet; repeat at 4-in. intervals. Around mounds of filling, brush pasta with water. Place a second pasta sheet over the first, starting at a short end and easing pasta over filling, gently pressing out air and sealing pasta around each mound of filling as you go.
Trim long sides of pasta sheet with a pastry wheel or knife so sheet is 4 in. wide. Cut ravioli between filling to make 4-in. squares. Transfer ravioli to parchment-lined pan and cover with plastic wrap; also gather and wrap pasta scraps. Continue shaping ravioli, rerolling scraps according to directions for Fresh Pasta Dough and stacking one more layer of parchment over first (add another pan if needed), until you've used all the filling; you should have 24 to 30 ravioli and may have leftover pasta dough. (If dough scraps become too dry to reroll, crumble into food processor and pulse with 1 tsp. water at a time until moistened.)
To serve: In a saucepan, boil broth until reduced by a third. Add butter; keep warm.
Preheat oven to 150° and set 8 wide soup plates or rimmed dinner plates in oven to warm. Bring 2 large pots (8 to 10 qt. each) of generously salted water to a rolling boil and add 1 tsp. olive oil to each. Divide ravioli between pots, reduce heat so water boils gently, and cook ravioli, occasionally pushing down into the water, just until al dente (test a corner of one to check), 5 to 7 minutes.
Set out soup plates. Using a slotted spoon, transfer 3 ravioli from water to each plate. Ladle broth over ravioli, sprinkle with parsley, and serve with parmesan.
*Shortcuts: Buy 2 3/4 lbs. peeled chunks of butternut squash instead of a whole squash. Buy semolina in the baking aisle of well-stocked markets. Instead of making pasta, buy about 2 lbs. fresh ravioli or lasagna sheets from a well-stocked grocery store or Italian deli, or from freshpasta.com ($79 for 16 oz.; 5-lb. minimum order). You may need to cut the ravioli in slightly different dimensions to make at least 24, and you may have leftover filling. For a recipe for chicken broth, see sunset.com/chickenbroth.
Make ahead: Make filling (through step 2) and chill overnight. Fill ravioli (through step 4) and chill them as long as 1 day, or freeze on pans until firm, transfer to bags, and freeze up to 3 weeks.
Note: Nutritional analysis is per serving.