Cut mushrooms into ¼" slices.
Peel and halve shallot. Slice thinly.
Cut broccoli into bite-sized pieces.
Pat chicken breasts dry and, on a separate cutting board, cut into 1" dice. Season with ¼ tsp. salt and ¼ tsp.pepper.
Sear the Chicken
Place a medium non-stick pan over medium-high heat and add 1 tsp. olive oil. You may also use a cast iron skillet.
Add chicken to hot pan and stir occasionally until seared on two sides, 3-4 minutes.
Transfer chicken to plate. Chicken will finish cooking in a later step.
Reserve pan; no need to wipe clean.
Start the Vegetables
Return pan used to sear chicken to medium-high heat and add 2 tsp. olive oil. Add mushrooms and shallot to pan and stir occasionally until lightly browned, 2-4 minutes.
Add marsala and stir occasionally until mostly reduced, 2-3 minutes.
Stir in cream, broccoli, 2 Tbsp. water, and demi-glace. Season with ¼ tsp. salt and a pinch of pepper.
Finish the Skillet
Return chicken and any accumulated juices to pan. Bring to a simmer.
Simmer until sauce is thick enough to coat the back of a spoon and chicken reaches a minimum internal temperature of 165 degrees, 4-5 minutes.
Stir in peas until warmed through, 1 minute.