Set oven rack about 6 inches from the heat source and preheat the oven's broiler.
Blend chiles with juices, garlic, vinegar, honey, pinch salt, and pinch black pepper in a blender until smooth.
Melt butter in a saucepan over medium heat. Whisk flour into into butter and stir until mixture is thick and flour cooks slightly, about 2 minutes. Slowly pour milk into butter-flour mixture, whisking constantly, until mixture thickens and is just beginning to bubble, 3 to 5 minutes. Add 1/2 teaspoon salt and 1/2 teaspoon black pepper; remove from heat.
Stir pepperjack cheese into milk mixture until cheese is melted and mixture is smooth. Pour cheese sauce into a baking dish; spread goat cheese slices over the sauce.
Bake in the preheated oven until dip is golden and bubbling, 3 to 5 minutes. Drizzle chile sauce over the hot dip.