Peel, cut in half, and place potatoes in a large pot of water. Bring to a slow boil and cook until the potato pieces are very fork-tender.
While the potatoes are cooking, heat olive oil over medium heat in a large pan and add the diced onion. Cook for 5 minutes or until translucent. Add the finely chopped celery and cook for 6-8 minutes or until the celery is tender. Remove the onions and celery from the pan and set aside.
In the same pan and over medium heat, add the breakfast sausage meat (no casing) to the pan, and using two forks, break apart the sausage meat into small pieces while cooking. Cook through until meat is lightly browned. Using a slotted spoon, remove the cooked sausage meat and set aside.
Preheat oven to 350 degrees.
Drain the potatoes and mash them with the butter, milk, and1 teaspoon of salt. If you like a creamier consistency, add more milk a little splash at a time.
In a large mixing bowl, add the mashed potatoes, cooked sausage, and cooked onion and celery mixture. Add the ground black pepper and mix well to combine. Taste the mixture and adjust the seasoning if needed. Place potato mixture into a baking dish and cover.
Place the covered baking dish into the oven. *If the mixture looks dry, add a little chicken broth and stir to combine.
Bake covered in oven for 45 minutes. If you like a crust on the top, remove cover and bake for another 15 minutes.