Easy side: Prepare frozen sweet potato fries as directed. Stir together 1 (14.5-oz.) can fire-roasted diced tomatoes with garlic, drained; 1/2 cup ketchup; 1 garlic clove, minced; and 1/2 tsp. dried rosemary. Serve with fries.
Prepare Herb Mayonnaise: Combine all ingredients. Chill until ready to use.
Prepare Sandwiches: Spread Herb Mayonnaise on 1 side of each bread slice. Layer 4 bread slices, mayonnaise sides up, each with 1 cheese slice, 1 Tbsp. red bell peppers, 1 rounded tablespoonful artichoke hearts, and 1/4 cup arugula. Top with remaining cheese and bread slices, mayonnaise sides down. Spread butter on outside of each sandwich.
Cook sandwiches in a large nonstick skillet or griddle over medium-high heat 3 to 4 minutes on each side or until lightly browned and cheese is melted. Serve immediately.