Cook the bacon in a large saucepan over medium heat until crisp, about 5 minutes. Stir in the shallots and half of the dill and cook until the shallots are soft, about 3 minutes.
Add the potatoes, carrots, 4 cups water and 1 teaspoon salt. Increase the heat to medium high, cover and bring to a simmer. Cook until the potatoes and carrots are almost tender, about 6 minutes. Add the mushrooms and Brussels sprouts and cook until all of the vegetables are tender, about 6 more minutes. Meanwhile, whisk the egg yolks, half-and-half and wine in a small bowl.
Reduce the heat to medium low, add the salmon and cook until opaque, 2 to 3 minutes. Gently stir in the egg mixture and cook until the soup thickens slightly, 1 to 2 minutes. Season with salt and pepper. Divide among bowls and top with the remaining dill.