Acorn Squash Stuffed with Mushrooms and Goat Cheese

3 tablespoons olive oil, divided2 white or green acorn squash (about 2 lb. each), halved lengthwise, seeds removed1 teaspoon kosher salt, divided½ teaspoon black pepper, divided8 ounces white button or cremini mushrooms, trimmed and chopped1 large shallot, chopped5 ounces spinach5 slices sandwich bread, cut into ½-in. pieces4 ounces goat cheese, divided5 ounces mixed greens1 teaspoon lemon juicePreheat oven to 425°F.Brush 1 tablespoon oil on cut side of squash halves; season with ½ teaspoon salt and ¼ teaspoon pepper. Place squash, cut side down, on a parchment-lined baking sheet; bake until slightly tender, 20 to 25 minutes. Remove from oven; turn cut side up.Meanwhile, heat 1 tablespoon oil in a large skillet over medium-high. Add mushrooms and shallot; cook, stirring occasionally, until tender, about 5 minutes. Add spinach; cook until wilted, about 1 minute. Season with ¼ teaspoon salt and ⅛ teaspoon pepper. Remove from heat and fold in bread and cheese.Divide mushroom mixture among squash halves, return to oven, and bake until tender, 8 to 10 minutes. Increase temperature to high broil. Broil until lightly browned, 3 to 5 minutes.Toss greens with lemon juice and remaining 1 tablespoon oil, ¼ teaspoon salt, and ⅛ teaspoon pepper. Serve salad with squash.