Preheat the oven to 350 degrees. Brush a 9-inch square baking dish with olive oil and sprinkle with 2 tablespoons breadcrumbs. Place the artichokes cup-side up on the breadcrumbs and brush or drizzle with olive oil. Sprinkle with 1 tablespoon breadcrumbs and the parmesan.
Bake for 15 minutes; remove from the oven and preheat the broiler. Divide the sheep's milk cheese among the artichokes; sprinkle with the remaining 1 tablespoon breadcrumbs. Broil until the cheese starts to bubble and the topping browns, 3 to 4 minutes. Toss the salad greens with the balsamic vinaigrette in a bowl; serve the artichokes on top of the greens.
Photograph by Mark Peterson
Recipe courtesy Sandra Lee for Food Network Magazine