Cut a small slit in each pepper, and carefully remove seeds. Rinse peppers with cold water; drain on paper towels.
Cut cheese into 18 pieces; insert 1 piece into each pepper.
Combine cornmeal and next 3 ingredients in a small bowl; add 1 tablespoon oil and beer, stirring until smooth. Let stand 10 to 15 minutes.
Pour oil to depth of 3 inches into a skillet or deep fat fryer; heat to 350°. Dredge peppers in 1/2 cup flour; then dip into batter. Fry 3 to 4 minutes or until golden brown, turning occasionally. Serve immediately.