In a 6-qt. stockpot, cook linguine according to package directions, adding peas during the last 2 minutes of cooking. Meanwhile, in a small saucepan, whisk egg, milk, red pepper, pepper flakes and pepper until blended; cook and stir over medium-low heat until mixture is just thick enough to coat a spoon and a thermometer reads at least 160°. Stir in 1/4 cup cheese and bacon; remove from heat.
Drain linguine; return to pot. Add sauce and toss to coat. Serve with remaining cheese.