Combine flour and pepper; dredge chicken in flour. Melt 3 tablespoons butter in the large skillet you used for mushrooms (you can use separate skillets if you like, but only if you love doing dishes) over medium to medium-high heat; brown chicken in butter on both sides, about 4-5 minutes each side. Remove chicken from skillet and set aside for now.

Add broth to skillet (be careful; it might steam heavily depending on how hot you've got it). Using a whisk, break up little browned bits on the bottom of the skillet. Reduce heat to low and cook for 5 minutes. Return chicken to skillet, sprinkle casually with basil (not so concentrated; you want the stock to infuse as well). Cover and simmer (braising) for 30 minutes.

Meanwhile, trim broccoli into florets. Steam in a steaming basket over the stove or in the microwave (place in a bowl, add a bit of water, cover, nuke.. test often. When done, drain. Do NOT use a steaming basket in here, as that will cause your microwave to.. catch fire).

Place broccoli in a buttered 9x9" baking dish. Remove chicken from skillet with a slotted turner (reserve the braising liquid) and place chicken on top of the broccoli in the baking dish. Spoon mushrooms over the chicken.

Stir the sour cream into the reserved braising liquid and whisk until smooth. Cook over low heat until thoroughly heated (do not boil!). Taste and correct seasonings (we add salt and more pepper). Pour sauce over chicken; sprinkle evenly with Parmesan cheese. Place pan 6" from broiler and broil for 3-5 minutes or until top is golden brown and beautiful and delicious in every way.

Split the egg noodles, cooked, into two bowls and spoon the chicken divan over the top. Invite me over for dinner.