Heat a gas grill on high or prepare a hot charcoal grill fire.
In a large bowl, toss the hearts of palm, radicchio, and asparagus with 2 Tbs. of the olive oil, 1/4 tsp. salt, and several grinds pepper. Grill, flipping as needed, until nicely marked all over and tender, 4 to 5 minutes total. Set aside until cool enough to handle.
Meanwhile, in a small bowl, whisk the remaining 2 Tbs. olive oil with the lemon juice, zest, sugar, 1/4 tsp. salt, and a pinch of pepper.
Core the radicchio. Cut the radicchio, asparagus, and hearts of palm into pieces about 3 inches long by 1/2 inch wide. Return to the large bowl and toss with the prosciutto, Parmigiano, and 2 Tbs. of the vinaigrette. Serve drizzled with the remaining vinaigrette, if desired.
nutrition information (per serving):
16, Fat Calories
140, Saturated Fat
7, Monounsaturated Fat
7, Polyunsaturated Fat
Photo: Scott Phillips