This is a delicous real-food comfort food! It has a few more steps than I usually bother with, so it's easiest if you plan ahead to use mashed potatoes and vegetables leftover from another meal. It's versatile, so feel free to use whatever vegetables you like or have on hand.
For the Meat Layer: Cook ground beef in a cast-iron skillet until no pink remains. Using a slotted spoon, remove browned meat into a casserole (about 9 x 11). Drain grease from pan. Next, heat 1 teaspoon of olive oil in skillet; add mushrooms and saute about 5 minutes, or until browned. Combine cooked mushrooms with broth, thyme, salt and pepper in a high-powered blender; blend 10 seconds or until smooth. Pour over meat evenly.
For the Vegetable Layer: In the cast-iron skillet, heat the remaining 2 teaspoons of olive oil on medium heat. Saute onion, carrots and celery for 5 minutes, or until tender. Add green beans and saute a few minutes more until tender. Spread vegetables evenly over the meat layer.
For the Garlic Mashed Potato Layer: Pour water into the insert of a 6 or 8-quart Instant Pot. Place a steamer basket into the Instant Pot insert. Place potatoes in the steamer basket. Set to manual, high pressure for 9 minutes; then quick release the pressure. Carefully remove hot potatoes to a bowl. Drain water and remove the steamer basket. On the Instant Pot's saute function, melt butter in the bottom of Instant Pot, then add garlic and saute for 1 minute. Return potatoes to Instant Pot insert; add milk and mash until smooth. Top vegetable layer with garlic mashed potatoes.
You can refrigerate the assembled pie at this point. When ready, bake at 375 for 25 to 30 minutes, or until heated through.