In a large skillet, heat oil over medium. Add onion, garlic, and cumin; cook, stirring occasionally, until onion is tender, 5 to 6 minutes.
Add squash, and cook, stirring occasionally, until mixture is slightly thickened, 2 to 3 minutes. Stir in beans and spinach. Cook until warmed through, 4 to 6 minutes; season with salt and pepper, and set aside.
Stack tortillas, and wrap in a double layer of damp paper towels; microwave until hot, about 2 minutes. Place tortillas on a work surface. Spoon goat cheese, then salsa in a line down center of each tortilla.
Spoon bean mixture on top of salsa. Fold side of tortilla closest to you over filling, then fold right and left sides in toward center; tightly roll up burrito. Cut burritos in half, and serve with more salsa.