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Brush pork with olive oil. Sprinkle pork with fines herbes (or basil) and salt; rub in with your fingers.
Prepare grill for indirect grilling. Test for medium-high heat above drip pan. Place pork on grill rack over drip pan. Cover and grill for 30 to 35 minutes or until pork juices run clear (155°F). Remove from grill. Cover with foil; let stand for 10 minutes. The temperature of the pork will rise 5°F during standing.
Meanwhile, in a small saucepan, melt butter over medium heat. Stir in flour and white pepper. Add milk all at once. Cook and stir until slightly thickened and bubbly. Cook and stir for 1 minute more. Remove from heat. Stir in pesto.
To serve, slice pork. If desired, serve over hot cooked pasta tossed with spinach. Spoon sauce over pork.