Preheat oven to 425°F. Combine buttermilk, garlic, 1 teaspoon of the salt, and 1/2 teaspoon of the pepper in a large ziplock plastic freezer bag; add chicken, seal bag, and toss to coat. Let stand at room temperature 30 minutes.
Combine potatoes, haricots verts, and shallots in a large rimmed baking sheet. Drizzle with 2 tablespoons of the oil, and sprinkle with remaining 1/2 teaspoon each of salt and pepper. Stir to coat, and spread in a single layer. Bake in preheated oven until potatoes and haricots verts are browned and tender, about 20 minutes, stirring once after 15 minutes.
Combine panko and 2 tablespoons of the parsley in a shallow bowl. Remove chicken from plastic bag, discarding any mixture in bag. Dredge chicken tenders in panko mixture, pressing to adhere.
Heat 1 tablespoon of the oil and 1 1/2 tablespoons of the butter in a large skillet over medium. Add half of chicken; cook until golden brown and done, 3 to 4 minutes per side. Remove to a serving platter; wipe pan, and repeat with remaining 1 tablespoon oil, 1 1/2 tablespoons butter, and half of chicken. Serve chicken with potatoes and haricots verts. Top chicken and vegetables with remaining 1 tablespoon parsley.