Position rack in upper third of oven. Preheat to 450°F.
Place squash cut-side down in a microwave-safe dish and add ¼ cup water. Microwave, uncovered, on High until the flesh is tender, 10 to 12 minutes. (Alternatively, place squash halves cut-side down on a rimmed baking sheet. Bake in a 400°F oven until tender, 40 to 50 minutes.) When cool enough to handle, scrape the squash from the shells into a large bowl. Add ¼ teaspoon each salt and pepper; stir to combine.
Meanwhile, heat oil in a large skillet over medium heat. Add onion and cook, stirring, until softened and beginning to brown about 5 minutes. Add broth, garlic, thyme and the remaining ¼ teaspoon each salt and pepper. Cook, stirring, until the onions are very soft and the liquid has evaporated, about 5 minutes more. Transfer to the bowl with the squash; stir in beans and 1 cup cheese.
Place the squash shells on a large rimmed baking sheet. Divide the filling between the shells and sprinkle with the remaining ¼ cup cheese.
Bake until hot and the cheese has melted, about 10 minutes. Turn the broiler on High and broil until the cheese starts to brown, about 2 minutes more. Sprinkle with parsley before serving, if desired.
