1. Count chilies and divide sliced cheese and beef into as many portions. Roll each portion of cheese around a portion of beef and stuff into a chili. Lay chilies side by side in an oiled shallow 9- by 13-inch casserole.
2. In a blender, whirl eggs, milk, flour, garlic, and 1/2 teaspoon salt to blend. Pour over chilies.
3. Bake in a 350° oven for 25 minutes. Sprinkle with shredded jack cheese and continue to bake until egg mixture no longer jiggles around chilies when casserole is gently shaken, about 2 minutes more.
4. Scoop onto plates and add salsa and salt to taste.