To prepare brine, place 2 teaspoons tea leaves on a double layer of cheesecloth. Gather edges of the cheesecloth together, and tie securely.
Combine 3 cups apple juice and next 5 ingredients (through bay leaf) in a large saucepan, and bring to a boil. Cook for 1 minute, and remove from heat. Add cheesecloth bag; cover and steep 5 minutes. Discard cheesecloth bag. Add 3 cups water, and cool to room temperature. Pour liquid into a large heavy-duty zip-top plastic bag. Add pork tenderloins to bag; seal and marinate in refrigerator 8 hours or overnight, turning the bag occasionally.
To prepare chutney, bring 2 cups juice to a boil in a large saucepan. Remove from heat. Stir in 2 teaspoons tea leaves, and steep for 2 minutes. Strain juice mixture through a sieve into a bowl; discard solids. Reserve juice mixture.
Heat butter and 1 teaspoon oil in pan over medium-low heat. Add onion; cook for 20 minutes or until golden brown, stirring frequently. Stir in apple; cook 5 minutes. Add reserved juice mixture, raisins, and next 8 ingredients (through ground cloves). Bring mixture to a boil over medium-high heat; reduce heat to medium. Cook 30 minutes or until apple is tender and mixture is thick. Remove from heat.
Preheat oven to 350°.
Remove pork from bag; discard brine. Pat pork dry with paper towels. Brush pork with 1 teaspoon oil; sprinkle on all sides with 1/2 teaspoon white peppercorns and 1/2 teaspoon black peppercorns. Place pork on a broiler pan coated with cooking spray. Bake at 350° for 40 minutes or until a thermometer registers 160° (slightly pink). Place pork on a platter, and let stand for 5 minutes. Cut pork across the grain into thin slices. Serve with chutney.