In a 5- to 6-quart pan, blend 1 cup polenta, 2 cups fat-skimmed chicken broth, 1 cup water, and 1/2 cup evaporated nonfat milk. Stir over high heat until mixture boils, then reduce heat and simmer, stirring often, until polenta is smooth to taste, about 15 minutes. Simmer, stirring often, until mixture is thick enough to hold a trough for about 5 seconds when you draw a spoon across the pan bottom, about 20 minutes total. Stir in all the shredded parmesan cheese, and add salt and pepper to taste.
Scrape the polenta into a lightly oiled 8-inch square pan, and spread smooth. Cover loosely and chill until firm, at least 1 hour. If making up to 1 day ahead, cover airtight and chill.
Quickly invert pan with polenta onto a cutting board; lift off pan. With a long, sharp knife, cut polenta into 6 or 7 equal strips (wipe knife clean frequently). Cut polenta strips in half crosswise and pull apart.
Put 1/3 to 1/2 cup seasoned fine dried bread crumbs on a plate. Gently roll polenta sticks, 1 at a time, in crumbs. Lay slightly apart on a lightly oiled 12- by 15-inch nonstick baking sheet. Mist sticks lightly with cooking oil or olive oil spray.
Bake polenta sticks in a 375° oven until browned and crusty, 45 to 50 minutes. Transfer to a platter or plates with a spatula.