Preheat oven to 375°F.
Place biscuit cubes in a large mixing bowl and set aside.
Grease the inside of a 9”x 12” baking dish with butter and set aside.
Pour 1 tablespoon oil into a large skillet and place over medium-high heat. Add mushrooms and sauté for about 3 minutes. Transfer mushrooms into a mixing bowl with the biscuit cubes.
Add remaining oil to skillet and sauté onion, garlic, bell pepper, and broccolini for about 5 minutes. Season with salt and pepper.
Add vegetable mixture to the mushrooms and biscuit cubes. Add tomatoes and thyme and gently toss everything together.
Place eggs and milk in a small bowl and whisk together. Pour egg mixture over biscuit and vegetable mixture, season with salt and pepper and fold together until fully incorporated.
Pour mixture into the prepared baking dish and allow pudding to sit for 30-45 minutes, to ensure all the liquid soaks up into the bread.
Sprinkle the surface with Parmesan and bake for 40 to 50 minutes or until the pudding has set and the surface has turned golden brown. Allow pudding to cool for 5-7 minutes. Serve.