Preheat the oven to 425 degrees. Line a large baking sheet with foil. In a measuring cup, whisk together the oil, vinegar, dijon, garlic, salt, and pepper until combined. Place all the veggies in a large bowl or ziplock bag. Toss with the vinegar mixture and allow to marinate in the fridge for at least 20 minutes or longer if desired.
Roast the marinated vegetables for 20 minutes, or until soft but not mushy.
To prepare the sandwiches, toast or grill the slices of bread. Then, layer them as follows: 1 slice of bread, a Tablespoon or so of the artichoke spread, prepared veggies, second slice of bread, slice of cheese, more veggies, and then the last slice of bread with another layer of artichoke spread on it.
Serve sandwiches warm with plenty of napkins!