Sift together dry ingredients. Stir in cheese, basil and orégano. Cut in shortening to make coarse crumbs. Add milk, tomato paste and egg; stir with fork until dough follows fork around the bowl.
Knead on floured board five or six times. Roll dough ½" thick. Cut in 1" rounds (we used a doughnut hole cutter). Press dough around franks to form cups.