Veggie Italian Hoagies

1 cup drained jarred giardiniera, finely chopped, plus some brine from the jar
1 cup mayonnaise
4 (8-inch) soft Italian sub rolls, split
4 large meaty tomatoes, sliced 1/2 inch thick
Kosher salt
1 head of iceberg lettuce, thinly shredded
Freshly ground black pepper
Olive oil (for drizzling)

Mix giardiniera into mayonnaise in a small bowl. Thickly spread some giardiniera mixture over the bottom half of each roll. Top each with tomato slices; season with salt. Layer on a thick tuft of shredded lettuce; season lettuce with salt, pepper, and a splash of reserved giardiniera brine (about 1 Tbsp. per sandwich). Drizzle with oil.