Bring a few inches of water to a boil in a large soup pot then drop a steamer basket into the pot. Add potatoes, place a lid on top, turn heat down to medium, and then steam potatoes for 5 minutes.
Add cauliflower florets on top of the potatoes, place the lid back on top, then steam for another 10 minutes or until cauliflower and potatoes are very tender. Transfer to a large food processor fitted with the whipping blade.
Meanwhile, warm milk and 2 Tablespoons butter in a small saucepan then add to food processor with salt and pepper. Process until vegetables very smooth then set aside.
For the Shepherd's Pie:
Preheat oven to 400 degrees. Brown ground beef, onions, garlic, salt, and pepper in a large skillet over medium-high heat then drain and return to the skillet. Sprinkle in flour then stir to coat and cook for 1 minute.
Add tomato paste, Worcestershire sauce, Tamari, and chicken broth to the skillet then bring to a simmer. Lower heat then continue to simmer until sauce has thickened, 5-6 minutes. Add frozen vegetables then more salt and pepper to taste.
Pour mixture into a large, oven-proof casserole dish then top with healthier mashed potatoes and dot the top with remaining Tablespoon butter, salt, and pepper. Place casserole dish on top of a baking sheet (in case the sauce overflows) then bake for 20-30 minutes, or until top is golden brown.