Preheat oven to 400 degrees.
Slice tomato into 1/4 inch slices.
Put sliced tomato in a bowl and drizzle with 1 t. olive oil. Season with salt and pepper. Evenly coat.
Cook tomato flat in skillet for a minute or two just to soften.
Slice the mushrooms about 1/4 inch thick.
Cut ends off shallot. Slice lengthwise into 1/4 inch strips.
Heat 3 T. olive oil in skillet over medium-high heat. Add mushrooms. Season with salt and pepper. Cook 4 to 5 minutes, till lightly browned.
Add artichoke hearts, roasted red peppers, and shallot. Add another 1 T. oil. Stir and cook 3 to 4 more minutes.
Put the nutritional yeast, grated cheese, garlic granules, and dried herbs in a small bowl and stir to mix.
Place flatbreads on an oiled baking sheet. (Can line with foil.)
Drizzle each with 1 T. oil and spread evenly.
Spread each evenly with the yeast/cheese mixture.
Spread basil pesto evenly over this. (If it's too thick to spread, mix in a little olive oil.)
Top with tomato slices.
Bake in oven until flatbreads are warmed and lightly toasted (2 or 3 minutes).
Spread vegetable mixture onto flatbreads.
Return to oven. Bake 2 or 3 more minutes until flatbreads are golden brown.
Cut each flatbread in half, to make 4 servings. (Can cut to smaller sizes to make them easier to handle.)