Crosswise cut bacon into 1/8- to 1/4-inch slivers. In large nonstick skillet cook bacon until brown and crisp. Drain off fat, reserving 1 tablespoon. Remove bacon from skillet. Drain on paper towels.
Return reserved bacon fat to skillet. Stir in onion. Cook, stirring occasionally, over medium heat for 4 to 5 minutes or until tender. Stir in carrot. Continue cooking for 3 minutes more. Remove from heat. Stir in vinegar and rosemary.
Set aside four pieces of artichoke. Stir remaining artichoke pieces into mixture in skillet. Cook, stirring frequently, over medium heat until liquid evaporates. Remove from heat. Stir in salt and pepper. Cool slightly.
Transfer artichoke mixture to food processor bowl. Cover and process until smooth. Let stand at room temperature for 30 minutes. Stir in half of the cooked bacon.
Cut reserved artichoke pieces into thin slivers. Spoon about 2 teaspoons artichoke mixture on each cracker. Garnish with artichoke slivers and remaining cooked bacon pieces.
