1. Preheat oven to 350°.
2. Heat a medium skillet over medium-high heat. Add 1 1/2 teaspoons oil; swirl to coat. Add shallots and rosemary; cook 1 minute or until lightly golden. Add brown sugar, vinegar, mustard, 1/4 teaspoon salt, and apricots; cook 12 minutes or until apricots are broken down and mixture is slightly thickened, stirring occasionally. Place 3 tablespoons apricot mixture in a small bowl; set aside.
3. Heat a large ovenproof skillet over medium-high heat. Add remaining 1 tablespoon oil to pan; swirl to coat. Sprinkle pork with remaining 1/4 teaspoon salt and pepper. Add pork to pan; cook 6 minutes, turning to brown on all sides. Brush pork with half of remaining apricot mixture (about 6 tablespoons). Place pan in oven; bake at 350° for 10 minutes. Turn pork; brush with remaining half of apricot mixture. Bake at 350° for 8 minutes or until a thermometer inserted into pork registers 145°. Place pork on a cutting board; let stand 5 minutes. Cut across the grain into 12 slices. Serve with reserved 3 tablespoons apricot mixture.