For Oven Dried Tomatoes: Place tomato halves on parchment paper-lined sheet pan, cut-side up. Drizzle with oil. Sprinkle with seasonings.
Bake in 300ºF standard oven 45 to 60 min. or until tomatoes have shrunk, and there is no visible moisture on them. Cool completely on pan at room temperature. Cover with parchment paper and set aside until ready to use.
For Onion Jam: Heat oil in large skillet on medium heat. Add onions; cook 15 min. or until softened, stirring occasionally. Add sugar; cook until melted and caramelized, stirring occasionally. Stir in vinegar; cook and stir until mixture thickens. Stir in salt and pepper. Cool completely at room temperature. Cover and set aside until ready to use.
For Black Pepper Mayo: Combine ingredients. Refrigerate until ready to use.
For Crispy Onions: Toss onions in combined flour and salt, shaking off excess. Fry in 350ºF oil 1 to 2 min. or until golden brown and crisp. Drain on paper towels. Hold at room temperature until ready to use.
For Breaded Cheese Patties: Combine flour and potato starch in bowl. Coat each cheese slice with mixture and set aside.
Add water and salt to remaining flour mixture in bowl. Whisk to combine. Dip cheese slices into batter, then immediately into combined cracker and bread crumbs in separate bowl, pressing crumb mixture gently into cheese. Place on parchment paper-lined sheet pan. Cover with plastic wrap and refrigerate until ready to assemble sandwich. (For thicker batter add less water.)
When ready to serve, fry patties in 350ºF oil 1 to 2 min. on each side or until golden brown. Drain on paper towels.
For each sandwich: Spread a bit of butter on 1 side of each bread slice. Toast until golden brown.
Spread 1 Tbsp. Black Pepper Mayo on toasted side of 1 bread slice. Top with 2 Tbsp. arugula, 1 oz. Onion Jam, 1 Breaded Cheese Patty, 3 Oven Dried Tomato halves and 1/4 cup Crispy Onions. Cover with second bread slice, toasted side facing onions. Serve immediately.