Cut mushrooms into ¼" slices. Mince garlic. Stem thyme. In a mixing bowl, combine ground turkey, seasoning blend, and half the Parmesan.
Start the Meatballs
Form turkey mixture into 10 golf ball-sized meatballs. Place a medium non-stick pan over medium-high heat. Add 2 tsp. olive oil and meatballs to hot pan. Stir occasionally until lightly browned on all sides, 3-4 minutes. Transfer to a plate. Meatballs will finish cooking in a later step. Reserve pan; no need to wipe clean.
Make the Broccoli Mash
Cut broccoli into florets if necessary. Add broccoli and garlic to boiling water and cook until bright green and very tender, 3-5 minutes. Drain in a colander and return to pot. Drain as much water from broccoli as you can. Mash until desired consistency. Add remaining Parmesan and a pinch of salt and pepper. Thoroughly combine. Cover and set aside.
Make the Sauce
Return pan used to start meatballs to medium-high heat. Add 1 tsp olive oil, mushrooms and thyme (reserve a pinch for garnish) to hot pan. Stir occasionally until mushrooms brown, 1-2 minutes. Combine ¾ cup water and cornstarch. Add water-cornstarch mix and demi-glace to pan and bring to a simmer.
Finish the Meatballs
Return meatballs to pan with sauce. Cover and cook until sauce slightly thickens and meatballs reach a minimum internal temperature of 165 degrees, 8-10 minutes.
Finish the Dish
Serve meatballs on a plate alongside broccoli mash. Top meatballs with sauce. Garnish with remaining thyme.