Set up a breading station: flour seasoned with salt and pepper in one bowl, beaten eggs in another, and panko breadcrumbs in a third.
Dredge each pounded chicken breast in flour, dip in the egg wash, and coat evenly with panko breadcrumbs.
Heat olive oil and 1 tablespoon of butter in a large skillet over medium-high heat. Pan-fry the chicken for 4-5 minutes per side until golden brown and cooked through (165°F internal temperature). Remove and keep warm.
In the same skillet, reduce heat to medium. Add the minced garlic and sauté for 1 minute until fragrant.
Pour in the white wine to deglaze the pan, scraping up any browned bits. Simmer for 2 minutes until reduced by half.
Stir in the heavy cream, then remove the skillet from the heat. Whisk in the remaining cold cubed butter, one piece at a time, until the sauce is smooth and emulsified.
Drizzle the warm garlic butter sauce over the plated chicken breasts and serve immediately.