Make sure your grains or pasta are fully cooked and fluffy before starting. Drop your chopped broccoli florets into a pot of violently boiling, salted water for exactly two minutes to blanch them. Drain immediately and run cold tap water over them to lock in that bright green color. Make sure they are drained completely dry.
Place a heavy-bottomed skillet over medium-high heat and pour in the olive oil. Toss your cubed poultry and sliced mushrooms into the hot pan in a flat layer. Let it sit completely undisturbed for three minutes to build a hard, golden crust. Stir briefly until barely cooked through, then move the meat and mushrooms to a clean plate
Turn your stove heat down to medium and melt the butter in the exact same skillet. Toss in the diced onions and minced garlic, cooking until the onions are soft and translucent. Sprinkle the dry flour directly over the wet onions and whisk aggressively for one minute to create a thick paste.
Slowly pour your cold milk and savory chicken broth into the skillet while whisking constantly. Keep stirring until the hot liquid simmers and thickens into a glossy, heavy gravy that coats the back of your spoon.
Pull the bubbling skillet completely off the hot stove to prevent the dairy from separating. Sprinkle your freshly grated cheddar, mustard powder, salt, and pepper into the warm gravy. Gently stir everything together off the heat until the cheese melts into a totally smooth, silky sauce.
Lightly grease a 9x13 inch (approx: 22x33cm) ceramic baking dish. Dump your cooked grains or pasta, blanched broccoli, and seared meat and mushrooms straight into the dish. Pour that ridiculously creamy cheese sauce directly over the top and fold everything together with a wooden spoon until fully coated.
Slide the heavy dish into an oven preheated to 375°F (approx: 190°C). Let it bubble away uncovered for 20 to 25 minutes. You want the edges to look aggressively bubbly and the top to turn a spotty golden brown. Let the hot pan rest on the counter for five minutes before serving so the sauce can thicken!