Bring a large pot of salted water to a boil—this will be used for both the broccoli and pasta, making efficient use of time and flavor. While waiting for the water to boil, cut the chicken breast into 1-inch cubes and chop the fresh parsley. Cut the broccoli into florets if not already prepared. Have all ingredients measured and ready before you begin cooking, as the next steps move quickly.
Once the water is boiling, add the broccoli florets and cook for 4-5 minutes until tender-crisp, then remove with a slotted spoon and set aside (this preserves the cooking water for the pasta). Add the egg noodles to the same pot of broccoli water and cook according to package instructions, then drain and set aside. I like to reserve about 1/4 cup of the pasta water before draining—it can help loosen the sauce if needed later.
Heat a large skillet over medium-high heat and add enough oil to coat the bottom (about 2 tablespoons). Once the oil is hot, carefully add the cubed chicken and cook for 4-5 minutes per side, stirring occasionally, until the chicken is golden-brown on the outside and cooked through. Don't crowd the pan—work in batches if needed to ensure proper browning. The golden crust develops flavor that will enhance the final dish.
Add the water, mustard, and honey directly to the pan with the cooked chicken, stirring to combine and scrape up any flavorful browned bits from the bottom of the pan. Reduce heat to low and let this simmer for 1-2 minutes to meld the flavors. Pour in the heavy cream and stir gently until fully incorporated, then continue cooking on low heat for another 2-3 minutes, stirring occasionally, until the sauce thickens slightly. I find that keeping the heat low prevents the cream from breaking and creates a silky, cohesive sauce.
Add the cooked broccoli and egg noodles from Step 2 to the pan with the chicken and sauce, gently folding everything together until well coated. Divide the chicken, noodles, and broccoli among serving bowls or plates, spoon the honey mustard sauce over top, and garnish with the fresh parsley.