Make Chili Lime Butter: Add the lime zest, softened butter, and chili powder to a small mixing bowl. Stir until the butter is smooth and the lime zest and chili powder are evenly mixed in.
Cut Cornbread: Cut the cornbread into wedges. Slice each wedge open through the middle so the cut sides can hold the flavored butter.
Butter Cornbread: Spread the chili lime butter over the cut sides of the cornbread wedges. Use an even layer so the cornbread toasts well without becoming too greasy.
Toast Cornbread: Place the buttered cornbread in a panini press or grill pan over medium heat. Toast for about 3 to 4 minutes, until warm and lightly golden with grill marks.
Season Chicken: Sprinkle the chicken breast cutlets evenly with kosher salt. Turn the chicken as needed so both sides are seasoned.
Heat Oil: Add the canola oil to a large skillet over medium-high heat. Let it heat until the oil looks shiny.
Cook Chicken: Add the chicken cutlets to the hot skillet. Cook for about 3 to 4 minutes per side, turning once, until browned and cooked through to 165°F.
Transfer Chicken: Move the cooked chicken to a plate. Keep it warm while you make the peach salsa mixture in the same skillet.
Add Salsa: Pour the medium salsa into the skillet. Stir with a wooden spoon and scrape up the browned bits from the bottom of the pan for about 1 minute.
Add Black Beans: Stir in the drained black beans. Simmer for about 2 minutes, until the beans are heated through.
Add Peaches: Add the diced peaches to the skillet. Stir gently and simmer for 2 to 3 minutes, until the peaches are warm and the salsa mixture thickens slightly.
Finish and Serve: Place the chicken on plates and spoon the peach black bean salsa over the top. Sprinkle with chopped cilantro, add sliced avocado, and serve with the toasted chili lime cornbread.