Brush large grill pan with vegetable oil and heat over medium-high heat.
Before grilling, toss veggies with olive oil, garlic, salt, and pepper. Grill vegetables in batches until nicely colored and soft, about 6 to 8 minutes per batch.
Cut bread in 6-inch pieces. Cut pieces lengthwise but don't go all the way through.
Spread a thick layer of ricotta on the bottom half of the bread. Sprinkle with salt.
Toss arugula with olive oil, balsamic vinegar and salt and pepper to taste. Place dressed arugula on top of ricotta layer. Then add the generous amounts of the different grilled vegetable.