Slice each chicken breast in half lengthwise to make 4 thin cutlets; season both sides with black pepper and the garlic powder.
Lightly dredge each cutlet in flour, shaking off excess.
Heat 1 tablespoon butter and the olive oil in a large skillet over medium-high heat until shimmering.
Add the chicken to the hot skillet and cook until golden, about 4–5 minutes per side; transfer the cooked cutlets to a plate and set aside.
Remove the pan from heat and pour in the chicken broth, soy sauce, honey, minced garlic, and the remaining 1 tablespoon butter; return the pan to medium heat and bring the sauce to a gentle simmer for about 1 minute.
Whisk the cornstarch with 1 teaspoon cold water until smooth, then stir it into the simmering sauce and cook, stirring, until the sauce begins to thicken.
Return the chicken and any accumulated juices to the skillet and simmer until the chicken is cooked through and the sauce is reduced to your liking, about 4–5 minutes; reduce heat if sauce is boiling vigorously.
Transfer chicken to plates and spoon sauce over the top, then serve immediately.