Preheat the oven to 400 degrees F (200 degrees C). Place chicken in the freezer until slightly frozen, about 15 minutes.

Place bacon in a large skillet and cook over medium-high heat, turning occasionally, until evenly browned and crisp, about 10 minutes. Drain bacon slices on paper towels and cut in half when cool.

Add mushrooms and garlic to the bacon fat and cook over medium-high heat, stirring occasionally, for about 2 minutes.

Mix 1/2 of the ale with 1 tablespoon cornstarch in a small bowl. Add to the mushroom mixture; cook and stir until slightly thickened, 2 to 3 minutes. Remove from the heat and set aside.

Combine milk and butter in a saucepan over medium heat; cook until butter melts and mixture is warm. Mix remaining beer with remaining cornstarch in a small bowl; add to the milk mixture along with chicken bouillon. Cook and stir until slightly thickened, 3 to 5 minutes. Remove from the heat and combine with mushroom mixture.

Preheat the oven to 400 degrees F (200 degrees C). Line a casserole dish with parchment paper.

Place eggs in a pie plate and mix with a fork until beaten. Place bread crumbs in a separate pie plate. Remove chicken from the freezer and cut a pocket into each breast. Stuff with bacon and Swiss cheese. Immediately dip in beaten egg mixture, then dredge in bread crumbs. Place in the prepared casserole dish.

Bake in the preheated oven until chicken is no longer pink in the center, about 20 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).