Sauté garlic, onion, and mushrooms in a medium skillet until soft. Remove the vegetables and set aside.
In the same skillet, melt 1/4 cup of butter over medium heat. Whisk in the cornstarch and cook 1-2 minutes. Add milk and broth.
Add vegetables back to the pan and bring to a boil. Turn the heat down a little and simmer the mixture (that means cook it just below boiling) until it is thickened. Remove from the heat and set aside.
Place the chicken breasts in a 9×13 baking dish in a single layer. Cover each breast with a slice of Swiss cheese.
In a medium bowl, mix the cooling mushroom mixture with the sherry and yogurt. Carefully spread over top of the chicken breasts without displacing the cheese slices.
Melt remaining 1/4 cup of butter. Add in the dill and crushed corn flakes. Lightly toast the corn flakes, then sprinkle the mixture onto the chicken breasts.
Bake for 45 minutes or until the chicken is cooked through.