Preheat outdoor grill or grill pan for direct grilling. Grill brats according to package directions. Transfer to cutting board and let stand 5 minutes; then slice into 1/4-inch slices.

Meanwhile, in medium bowl, whisk together eggs, milk, salt and pepper.

Heat oil in large nonstick skillet over medium-high heat. Add bell peppers and onion; cook 4 to 5 minutes or until vegetables are tender-crisp, stirring occasionally.

Reduce heat to medium. Add sliced brats and egg mixture to skillet. Cook 5 to 6 minutes or until eggs are cooked through, stirring and breaking up eggs with spatula frequently. Fold in cheese during last minute of cooking time. Serve immediately.