Preheat oven to 350°F with a rack set in the middle position. Pound the thick ends of chicken breasts between two sheets of plastic wrap to an even ½-inch thickness. Pat chicken dry and season with ¼ teaspoon pepper. Lay 2 prosciutto slices slightly overlapping on a cutting board, place one chicken breast on top, and wrap the prosciutto around the chicken. Repeat for all breasts.

Heat 1 tablespoon olive oil in a 12-inch oven-safe skillet over medium-high heat until just smoking. Add wrapped chicken and cook until prosciutto browns lightly, about 2 minutes per side. Remove chicken and place fontina slices on top.

To the same skillet, add half the asparagus with tips pointing in one direction and the other half with tips in the opposite direction. Toss with 1 tablespoon olive oil and season lightly with salt. Arrange chicken breasts on top of the asparagus. Bake for about 12 minutes, or until chicken reaches an internal temperature of 160°F and asparagus is tender.

In a small bowl, whisk together the remaining 3 tablespoons olive oil, vinegar, pecans, mustard, shallot, thyme, and a pinch of salt until well combined.

Remove skillet from the oven using potholders. Let the chicken rest for 5 minutes. Toss asparagus with half the vinaigrette. Serve chicken with asparagus, drizzling more vinaigrette on top, and pass any remaining dressing separately.