Place the potatoes on a baking sheet and bake for 1 hour and 15 minutes in a 350°f oven. Set aside until cool enough to handle. Cut the potatoes into 1-inch cubes.

Sauté the shallot, salt and pepper in olive oil for 5 to 8 minutes over medium heat. Add the stock, cover and bring to a boil. Reduce the heat and simmer, covered, on medium-low for 10 minutes. Add the baked potatoes and simmer for another 10 minutes.

In a bowl, whisk together the half-and-half, milk and flour. Add this mixture to the soup, stirring as you pour it in. Bring soup back to a boil and allow to simmer for 3 to 4 minutes.

Garnish each bowl of soup with grated cheddar cheese, sour cream and sliced green onion, or any other potato toppings that you enjoy.