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PreparationRoast tenderloin: Preheat oven to 500°F with rack in middle.
Mince and mash garlic to a paste with 1 1/4 teaspoon salt. Transfer to a small bowl and stir in paprika, cumin, oil, and 1 teaspoon pepper.
Pat tenderloin dry, then rub garlic mixture all over it. Roast in a roasting pan until an instant-read thermometer inserted diagonally 2 inches into center of meat registers 120°F, 25 to 35 minutes for medium-rare.
Transfer to a platter along with any pan juices and cool, loosely covered with foil, 30 minutes to 1 hour. (Internal temperature will rise to about 130°F as it rests.)
Make mayonnaise: Stir together mayonnaise, paprika, cumin, and 1/2 teaspoon pepper. Stir in meat juices and salt to taste
To serve: Cut meat into thick slices. Serve warm or at room temperature, with smoked-paprika mayonnaise.
Cooks' note:Smoked-paprika mayonnaise keeps, chilled, 2 weeks.