For the soup:

1. In a large Dutch oven or soup pot over medium-high heat, add 1 tbsp of the garlic-infused olive oil. (If using the traditional olive oil and garlic clove substitute, reserve the minced garlic cloves to the side until you add the veggies so they don't burn). Once the oil is shimmering, add the bratwurst. Sear until golden brown on the first side, about 3-4 minutes then flip and sear on the opposite side for 2 minutes. It's not necessary to cook the bratwurst all the way through as they'll finish cooking once they're added to the soup, you just want to get a good sear on the outside. Remove the bratwurst from the pan and reserve to the side.
2. Add the remaining tbsp of garlic-infused olive oil to the pan (or traditional olive oil). Add the carrots, potatoes, and mushrooms to the pan (along with the minced garlic if you are using it) and saute until the potatoes are just beginning to get lightly golden on the edges but aren't fully browned about 5-6 minutes.
3. Add the tomato paste to the pan and continue to saute for 1-2 minutes or until the tomato paste darkens. Add the chicken broth to the pan to deglaze, scraping the bottom of the pan to dislodge any tomato paste or crispy bits.
4. Add the sauerkraut along with its juice, dijon mustard, dill, caraway seeds, thyme, paprika, salt and bay leaf to the pot. Stir to combine.
5. Allow to come to a boil, then reduce the heat until it maintains a steady simmer. While the soup simmers, slice the reserved seared bratwurst into coins and reserve to the side. Once the potatoes are nearly tender, add the bratwurst to the pot to finish cooking. Once the bratwurst is cooked through and the potatoes are tender, taste for salt and adjust if needed. Carefully remove bay leaf.
6. Serve warm with rye croutons on top, and optional sour cream and fresh dill to garnish.

For the rye croutons: You can make these first, or dress and bake them while the soup simmers.

1. Preheat oven to 400 degrees F / 205 C. Line a baker's half sheet with parchment paper and reserve to the side.
2. Cut rye bread into cubes (about 1-1 1/2 inches each). Transfer the rye bread to the reserved sheet pan. Drizzle olive oil, salt, dill, and caraway seeds over top of the cubed bread and toss by hand to combine until evenly coated.
3. Transfer the pan to the oven to bake for 14-minutes, tossing halfway through, until evenly toasted. The croutons will continue to firm up slightly as they cool.