Combine butternut squash puree, ricotta, egg, ¼ cup Parmesan, salt, pepper, and nutmeg in a large bowl. Mix gently until just combined, then fold in flour gradually until a soft dough forms that's slightly sticky but manageable.
Dust a clean counter with flour and divide your butternut squash gnocchi recipe dough into four equal portions. Working with one piece at a time, roll into a ½-inch-thick rope, then cut into ¾-inch pieces using a sharp knife or bench scraper.
Bring a large pot of salted water to a rolling boil. Working in batches of about 12 gnocchi at a time, gently drop them into boiling water. They'll sink initially, then float to the surface after 2-3 minutes; cook for another minute after floating.
Transfer cooked gnocchi to a plate using a slotted spoon. Melt butter in a large skillet over medium heat and sauté minced garlic for 30 seconds until fragrant and golden.
Pour heavy cream and vegetable broth into the skillet, stirring to combine with garlic-butter base. Simmer for 2-3 minutes until sauce begins to reduce slightly, then add fresh sage and season generously with salt and pepper.
Gently add cooked gnocchi to the cream sauce, folding carefully to coat each piece without breaking them apart. Toss for 1-2 minutes until heated through and silky.
Divide among serving bowls and top with additional grated Parmesan and cracked black pepper for garnish.