With meat mallet, pound chicken breasts between sheets of waxed paper to ½ inch thickness. Season chicken with salt and pepper; sprinkle with rosemary. Drizzle olive oil evenly over chicken and, using fingers, rub herb and seasonings into chicken. Refrigerate until needed. Preheat broiler, gas or charcoal grill.
Prepare spicy chile mayonnaise by placing jalapenos and garlic cloves in small skillet over medium-high heat. Cook and turn as necessary to brown evenly and chiles and garlic are softened. Set garlic aside to cool, then peel. Transfer chiles to small bowl of water and keep submerged for 20 minutes.
Place garlic, vinegar and honey in bowl of food processor fitted with metal blade. Pulse to combine. Remove chile from water, stem, seed and add to processor. Pulse to chop and then puree until mixture forms a rough paste. Add mayonnaise, salt and pepper and pulse evenly to blend. Transfer to small bowl and refrigerate until needed.
Place chicken breasts under broiler or on grill and cook, turning once, until done, about 3 minutes per side. Remove from heat and cover with foil. Finish sandwiches by lightly toasting each side of rolls. Spread spicy 2 tablespoons chile mayonnaise on bottom half of rolls; top each with chicken breast half. Add 2 slices of bacon to each sandwich; divide arugula among sandwiches. Secure sandwiches with tops of buns and serve immediately.