0 Spread the pumpkin onto a double layer of paper towels. Top with two more layers, press firmly to draw out moisture. (Repeat with a fresh set of paper towels on top if necessary). Repeat this same process with the cottage cheese.
1 Transfer the pumpkin and the cottage cheese to a large bowl. Add the eggs, nutmeg, and 3/4 teaspoon of the salt and whisk to combine. Whisk in the Parmesan.
2 Add 1 1/2 cups of the flour and stir with a wooden spoon until just incorporated. If the dough is way too sticky to handle, add up to 1/2 cup more flour a few spoonfuls at a time.
3 Transfer to a lightly floured work surface and knead a few times until it comes together into a ball. Let rest while you sauté the Brussels sprouts. (At this point, you can also wrap the dough in plastic wrap and refrigerate overnight).
4 Heat 1 tablespoon of the oil in a 12-inch skillet (I prefer cast-iron) over medium-high heat. Add the Brussels sprouts, season with the remaining 1/2 teaspoon salt and several grinds black pepper, and arrange cut side down. Cook, undisturbed, until browned underneath, 3 to 5 minutes. Stir and continue cooking until browned all over and just tender, 3 to 5 minutes more. Transfer to a bowl or plate.
5 Bring a large pot of salted water to a boil. Line a baking sheet with parchment paper; dust the parchment with flour.
6 Cut the gnocchi dough into four sections with a floured knife or bench scraper. Using floured hands, roll each section into a long rope, dusting with more flour as needed. Cut into small (about 1/2-inch) pieces. Transfer to the prepared baking sheet.
7 When the water is boiling, use the parchment paper to funnel the gnocchi into the water. Cook until they rise to the surface, then cook 1 minute more (2 to 3 minutes total).
8 Meanwhile, heat the remaining 1 tablespoon oil in the now-empty skillet over medium-high. Use a slotted spoon or spider, transfer the gnocchi from the water to the skillet and arrange in a single layer. Cook, undisturbed, until golden brown on one side, 2 to 3 minutes. Add the butter, red pepper flakes, and a drizzle of honey or maple syrup and cook, stirring, until the butter is browned and nutty smelling, 2 to 3 minutes.
9 Stir in the Brussels sprouts and cook until warmed through. Top individual portions with more Parmesan.
