"Agrodolce" means "sweet and sour" in Italian and refers to the sweet and tangy glaze that coats the cipollini onions (flat, yellow Italian onions) that accompany an always-popular beef tenderloin.
Place onions, butter, sugar, 1/2 teaspoon salt, 1/4 teaspoon pepper in single layer in a large straight-sided saute pan; add 1 inch of water. Simmer over medium heat, covered, 1 hour; the onions should be soft. Uncover; add vinegar. Cook, turning occasionally, until liquid evaporates and onions caramelize, about 1 hour. Stir in thyme leaves. Set aside.
Heat oven to 400 degrees. Coat meat with remaining salt and pepper. Place saute pan with ovenproof handle over high heat. Add olive oil; heat until almost smoking. Place beef in pan; sear until well browned on all sides. Transfer to oven; roast 30 to 40 minutes, or until internal temperature is 130 degrees for medium rare. Allow to rest at least 10 minutes before slicing. Beef may be served warm or at room temperature. Slice just before serving. Place on platter with reserved cipollini onions; garnish with thyme sprigs.
Serve with steamed asparagus. Pearl onions may be substituted for the cipollini.