Peel and dice the sweet potatoes into 1" pieces. Place them in a pot and cover with water and a sprinkle of salt. Cook until fork tender, this should take less than 15 minutes.
While the potatoes are cooking, cook and crumble the ground beef over medium heat. When it is almost browned, drain off any fat and add the onions, and carrots.
Cook for 2-3 minutes then add the minced garlic, parsley, thyme, basil, ½ teaspoon salt, and ¼ teaspoon black pepper. Cook an additional 2-3 minutes until the onions are soft.
Add the tomatoes and balsamic vinegar. Cook until the liquid is reduced, as needed. Stir in the peas. Taste and then season with salt and pepper. Adjust as desired. Remove from heat and set aside.
Preheat the oven to 350°F. Drain the potatoes and mash gently with a potato masher. Season with ½ teaspoon salt and ¼ teaspoon pepper to taste. Add just a splash of milk and stir until the potatoes are smooth and fluffy.
Layer the beef mixture into a baking dish and then top with the mashed sweet potatoes. Bake for 25 minutes, until hot and bubbling.