Preheat oven to 375° F. Cut acorn squash in half, lengthwise; scoop out seeds and discard. Rub 1 Tbsp. oil over flesh and season with 1/2 tsp. salt. Place flesh-down on a baking sheet; Bake for 45 minutes.
Meanwhile, heat remaining 1 Tbsp. oil in a large non-stick skillet over medium. Add shallot and mushrooms; cook 5 to 6 minutes, until tender. Add garlic, 1/2 tsp. salt, and 1/4 tsp. pepper; cook 1 more minute. Add milk; simmer until slightly reduced, about 10 minutes.
Combine quinoa and broth in a saucepan and bring to a boil. Reduce to a simmer, cover and cook until broth is absorbed, about 10-15 minutes. Stir quinoa and 2 Tbsp cheese into mushroom mixture.
Fill the hollow center of each squash half with quinoa mushroom mixture. Top with remaining parmesan cheese. Bake for 15 minutes, or until cheese is melted.
Meanwhile, pour balsamic vinegar in a small saucepan and bring to a boil. Reduce to a simmer and cook 10 minutes. Remove from heat and allow to thicken, about 5 minutes.
Drizzle balsamic over squash, and garnish with herbs.