Steam broccoli for 5 minutes until crisp-tender. (I steam in the microwave covered with plastic wrap for 4-5 minutes.) More or less time may be needed, depending on thickness of broccolini. Drain in colander.
Slice the chicken lengthwise in half. Salt and pepper each side.
In a medium frying pan, melt the butter; whisk in the flour and cook for 1-2 minutes (until no longer lumpy).
Gradually whisk in chicken broth, sherry cooking wine and milk or half and half, until mixed well. Bring to a boil and then reduce to a simmer until the sauce is thickened.
Add curry powder. Add 2 cups of the cheese; blend and whisk until combined. Salt and pepper to taste.
Prepare the dish:
Add 1 cup of curry sauce to the bottom of a prepared (sprayed) 9×13 pan.
Roll a few sprigs of broccolini in each chicken breast; place seam side down in the pan. Continue until pan is full. Heavily salt and pepper both sides.
Pour sauce over top and sprinkle with Panko crumbs. Cover with aluminum foil. Make several slits in aluminum foil for steam to escape.
Bake for 30 minutes; remove foil and bake an additional 10 minutes to allow the Panko crumbs to get golden.