Cut broccoli into bite-sized florets. Peel and halve shallot. Slice halves into a small dice. Mince garlic. Pat chicken breasts dry, season both sides with ½ tsp. salt and a pinch of pepper.
Toast Almonds and Sear Broccoli
Place a medium non-stick pan over medium-high heat and add almonds. Stir occasionally until golden brown, 2 minutes. Remove from burner and transfer almonds to a plate. Wipe pan clean and return to medium-high heat. Toss broccoli in a mixing bowl with cooking spray, ¼ tsp. salt, and a pinch of pepper. Add broccoli to hot pan and cook undisturbed for 2 minutes. Transfer broccoli to one side of prepared baking sheet and top with shallot (reserve 1 Tbsp. for sauce), garlic, and a pinch of salt. Reserve pan; no need to wipe clean.
Sear the Chicken
Return pan used to sear broccoli to medium-high heat and add 1 tsp. olive oil. Add chicken to hot pan and sear undisturbed, 2-3 minutes. Place on empty half of baking sheet. Roast until broccoli is tender and chicken reaches a minimum internal temperature of 165 degrees, 5-7 minutes. Reserve pan; no need to wipe clean.
Make the Sauce
Combine ½ cup water, cream, and cornstarch. Return pan used to sear chicken to medium-low heat. Add reserved shallot to hot pan and stir constantly until shallot is translucent, 1-2 minutes. Add cornstarch slurry and cheese to pan and bring to a boil. Once boiling, stir constantly 1 minute. Remove from burner. Season with a pinch of salt.
Finish the Dish
Place broccoli on a plate and garnish with almonds. Place chicken next to broccoli. Drizzle sauce on top of chicken and broccoli. Alternatively, place sauce on plate first, then chicken and broccoli.