Pat the chicken breasts dry with paper towels, then brush them generously with half of the Caesar dressing, coating all sides evenly.
Heat your grill or grill pan over medium-high heat, then place the chicken breasts on the grill, cooking for about 6-8 minutes per side until golden brown and cooked through. Baste occasionally with remaining dressing for extra flavor.
While the chicken is grilling, preheat your oven to 400°F (200°C). Toss the trimmed asparagus with 1 tablespoon of olive oil, minced garlic, salt, and pepper, then spread them out on a baking sheet.
Roast the asparagus in the oven, tossing halfway through, for about 12-15 minutes until they are tender and slightly crispy on the edges.
Meanwhile, sprinkle the toasted bread crumbs over the cooked chicken, pressing lightly to adhere and creating a crispy topping.
Once the chicken is done, let it rest for a few minutes, then slice or serve whole, with the roasted asparagus on the side.
Finish the dish with a drizzle of extra Caesar dressing if desired, and serve hot for a flavorful, textural contrast between tender chicken and crispy asparagus.