For apple cider brine, in large saucepan over medium heat bring water, salt, brown sugar, thyme, peppercorns, and cloves to boiling. Cook, uncovered, 2 to 3 minutes, stirring occasionally until sugar and salt are dissolved. Remove from heat; stir in apple cider and ice cubes. Cool.
Place pork chops in extra-large resealable plastic bag. Pour cooled brine on chops; seal bag. Refrigerate 6 to 12 hours, turning bag occasionally to marinate evenly. Drain chops; discard brine. Pat chops dry with paper towels. Lightly brush chops with olive oil.
Brush peppers and bread slices with olive oil. Add peppers to grill with chops. Grill directly over heat about 8 minutes, turning occasionally, until tender. Add bread to grill during last 2 to 4 minutes of grilling, turning once. Serve chops with peppers and bread. Makes 4 servings.