Snap off and discard woody bases from asparagus. Place asparagus in a steamer basket over boiling water or directly in a small amount of boiling water; cook about 3 minutes or until crisp-tender. Drain and rinse under cold water until cool; drain on paper towels.
Cut ham into 24 strips, about 8x1-1/2 inches each; set aside. Using a mortar and pestle or fork, mash olives, garlic, capers, olive oil, and vinegar into a chunky paste. Spread a heaping 1/4 teaspoon olive paste atop each ham strip. Lay 1 asparagus spear at 1 end of each slice of ham. Place a basil leaf and 2 strips red pepper next to asparagus. Roll ham tightly around fillings, covering each except for tops; repeat with remaining ingredients. Serve immediately or cover and chill for up to 4 hours. Makes 24 rolls.