Preheat oven to 400 degrees F (205 degrees C). Line two large rimmed baking sheets with parchment paper.
Cut Green Beans (1 cup) uniform bite-size pieces and blanch them.
Cut and slice Plum Tomato (3), Vidalia Onion (1), Button Mushroom (8), Bell Pepper (1), Broccoli Florets (3 cup), and Zucchini (1) into uniform bite-size pieces.
Place in a single layer in groupings on prepared trays. Brush the surface of all pieces with the Olive Oil (1/2 cup). Season with Coarse Kosher Salt (1 1/2 teaspoon) and Ground Black Pepper (1/2 teaspoon).
Place the Fresh Oregano (8 sprig) over each type of vegetable. Roast in the preheated oven for about 15 minutes until tender and slightly charred, rotating pans halfway through. Check often for charring. If one of the vegetables is finished before the others, remove it from the tray and allow the remaining veggies to finish roasting.
Melt Unsalted Butter (2 tablespoon) in an ovenproof skillet or baking dish. Add the roasted vegetables along with Monterey Jack Cheese (8 ounce) and Parmesan Cheese (1 ounce). Stir to combine. Place the skillet in the oven.
Bake for 15 minutes until the cheese is fully melted and bubbling around the edges.
If additional cheesiness is desired, sprinkle the remaining Parmesan Cheese (1 ounce) over the top. Place the skillet under the broiler for just one minute until toasty.
Serve immediately with naan, crusty bread or hearty chips.