Preheat the oven to 425 degrees F. Place the
squash halves in a large microwave-safe bowl with 1/4 cup water; cover loosely
with plastic wrap. Microwave until fork-tender, about 15 minutes.
Meanwhile, heat the olive oil in a medium saucepan
over medium-high heat. Add the onion and poblano and cook, stirring, until
slightly softened, about 2 minutes. Add the garlic, cumin, 1/2 teaspoon salt
and a few grinds of pepper; cook, stirring occasionally, until the vegetables
soften, about 3 minutes. Add the enchilada sauce and chicken. Bring to a simmer
and cook until the sauce slightly thickens, about 5 minutes. Stir in the
cilantro and season with salt and pepper.
Place the acorn squash cut-sides up in a
9-by-13-inch baking dish. Divide the chicken filling evenly among the squash
halves and top with the cheese. Bake until the cheese is lightly golden and
melted, 10 to 12 minutes. Top with sour cream and more cilantro.