Combine the milk, 1/2 cup of the Gruyère, and the agar in a heavy medium saucepan and bring to a boil over high heat, stirring to dissolve the cheese and agar. Boil for 2 minutes. Strain the mixture through a fine-meshed sieve lined with cheesecloth and into a bowl, then set aside to cool. Refrigerate until cold but not set, about 10 minutes. Rewhisk the mixture to loosen it if necessary.
Line a 5-inch square baking pan with plastic wrap. If you don’t have this size pan, use another container that allows the mixture to reach the depth of about 1 inch. Using an electric mixer with the whisk attachment or a large flexible whisk, whip the eggs whites with a touch of kosher salt in a large bowl until it becomes very thick and soft peaks form. Whisk in the cold milk- Gruyère mixture. Transfer the mixture to the prepare baking pan so that it is about 1 inch thick, then cover and refrigerate until it is cold and firm. Cut out 1-inch cubes, and then roll the cubes in the remaining 1/2 cup of Gruyère powder.
Preheat the oven to 375°F. Toss the bread cubes with the olive oil in a large bowl to coat. Place the bread cubes on a baking sheet and bake until they are toasted and very dark brown, turning them after the first 15 minutes so they brown evenly, about 30 minutes total.
Melt the butter in a heavy large saucepan over medium heat. Add the onions and bacon and sauté until pale golden, about 12 minutes. Add the toasted bread then stir in the chicken stock, 5 cups of the milk, vinegar, and mustard. Bring to a simmer and cook until the bread is soft, stirring occasionally, about 20 minutes.
Transfer the soup to a Vitamix and blend until the soup is very smooth, adding more of the remaining 1 cup of milk to thin the soup, if necessary. Season the soup to taste with salt and pepper.
Ladle the hot soup into 6 soup bowls, then place 3 Gruyère marshmallows on top of each bowl of soup and serve.