Preheat oven to 400°F. Line a rimmed baking sheet with parchment paper. Cut a medium butternut squash (about 2 to 2 1/2 pounds) in half lengthwise, scoop out seeds, and place cut side down on the prepared baking sheet.
Roast for 40 to 50 minutes until a knife slides into the thickest part with no resistance. Let cool for 15 minutes, then scoop the flesh away from the skin and blend in a food processor until completely smooth, about 45 seconds.
Measure out 1 1/2 cups of puree. If it looks loose or watery, spread it on a plate for 10 minutes to let excess moisture evaporate. Let cool to room temperature before using. Skip this whole step if using canned puree.
Plug in your Belgian waffle maker and set it to medium-high. It needs a full 10 minutes to reach temperature. Set your oven to 200°F and slide a wire cooling rack onto a baking sheet inside it to keep finished waffles warm.
In a large mixing bowl, whisk together the 2 cups flour, 2 tablespoons brown sugar, 1 tablespoon baking powder, 2 teaspoons pumpkin pie spice, 1/2 teaspoon cinnamon, and 1 teaspoon salt for a full 20 to 30 seconds. Break up any lumps of brown sugar. Set aside.
In a second large bowl, whisk the 3 eggs until fully blended and slightly foamy. Add the 1 1/2 cups cooled butternut squash puree and whisk until no orange streaks remain.
Pour in the 1 1/2 cups room temperature milk and whisk until smooth and pourable. Add the 2 teaspoons vanilla extract and 2 tablespoons maple syrup, then whisk to combine.
Stream in the 6 tablespoons melted butter while whisking constantly. Adding it slowly keeps it from seizing into little clumps against the cold puree.
Pour the wet mixture into the bowl of dry ingredients all at once. Fold with a silicone spatula using about 12 to 15 strokes, just until you no longer see dry flour. A few small lumps are exactly what you want. Fold in the 1/2 cup chopped pecans now if using, with three or four gentle strokes.
Let the batter sit on the counter for 10 minutes, uncovered. During this rest the flour hydrates fully and the baking powder starts working. If the batter becomes too stiff to pour, whisk in milk 1 tablespoon at a time.
Brush the waffle plates lightly with neutral oil once the iron is hot. Scoop about 1/3 cup of batter into the center of each waffle well. Deep Belgian pockets may take closer to 1/2 cup. Spread the batter gently toward the edges with the back of a spoon, stopping about half an inch from the rim.
Close the lid and cook for 4 to 5 minutes without opening it. Watch the steam rather than the clock. When the heavy stream of steam slows to a wisp, the waffle is close to done. You want a deep golden brown with crisp, set edges.
Lift the waffle out with a heatproof fork or silicone tongs, never a metal knife. Move each finished waffle to the wire rack in the warm oven. Never stack them on a plate. Re-grease the plates and repeat with the remaining batter.
Serve them hot with softened butter and warm maple syrup, plus a dusting of powdered sugar if you are feeling festive.