Baked Cheddar-Broccoli Rice Cups

quick-cooking rice, like Minute Rice (can substitute about 2 cups regular, cooked rice and omit the 1 cup stock below)

chicken stock

box frozen, chopped broccoli, thawed and excess water squeezed out

shredded cheddar cheese, divided

Homemade Ranch Dressing (see recipe), or store bought

eggs, lightly beaten

salt and freshly ground pepper to taste