Slice potatoes into 1/8" rounds. Toss potatoes on prepared baking sheet with 2 Tbsp. olive oil and spread into a single layer. Roast 15 minutes, flip potatoes, and roast 12-18 more minutes, or until browned. Remove from oven and toss hot chips with ranch seasoning (start with half, taste, and add more if desired). Transfer to a plate and set aside. Some potatoes may brown quicker than others, so watch closely towards the end of cooking to avoid burnt chips.

While potatoes are baking, core green tomatoes and cut into 1/3" rounds. Lay tomatoes on a large plate or tray and sprinkle both sides with sugar and 1/2 tsp. salt. Halve grape tomatoes. Halve and peel onion. Slice halves into thin strips (julienne).

Warm an outdoor grill or grill pan to medium-high heat. Lightly coat grill and green tomatoes with cooking spray. Working in batches if necessary, add green tomatoes to hot grill and cook 2-3 minutes on each side, or until slightly charred.

Use tongs to carefully place French rolls directly on oven rack and cook 2-4 minutes, or until warmed through and slightly toasted.

Spread mayo on inside of French roll. Add grilled green tomatoes to roll and top with arugula, onion (to taste), and grape tomatoes. Serve chips on side.