In a 3-4 Qt pot, heat olive oil on medium high. Add onions and garlic and cook until onions are translucent. Add both cans of tomatoes, white wine, salt and pepper. Continue to cook uncovered on medium high until most of the liquid is gone, stirring occasionally, about 15 minutes. Reduce heat to medium and add carrots and mushrooms. Cook uncovered for another 15 minutes, stirring occasionally. Remove from heat and stir in peas. Spread mixture into a 2 ½ Qt dutch oven or casserole dish.
Fill a 2-3 Qt pot with water and bring to a boil. Add potatoes and boil until a knife is easily inserted into the thickest part of the potatoes, about 15-20 minutes.
Drain the potatoes, returning them to the pot they were cooked in. Add butter, yogurt and salt. Using a hand mixer, blend potatoes to desired smoothness.
Spread mashed potatoes over top of the casserole with cooked vegetable mixture. Casserole should have enough room above the potatoes to allow for the bubbling of the vegetable mixture.
Move to the oven and bake at 350F for 50-60 minutes until potatoes at the center of the casserole are slightly browned. Serve immediately and enjoy!
