In a large pot, drizzle 1 tablespoon of the vegetable oil over medium heat. Add the sliced sausage if using and cook until golden and the fat has rendered. Remove to a plate with a slotted spoon, leaving the fat in the pan.
Add the onion to the pan and cook, stirring occasionally, until softened. Mix in the garlic and cook just until fragrant, 30 seconds to 1 minutes.
Pour in the chicken broth, followed by the potatoes, bay leaves, salt, and pepper. Bring to a boil, then reduce to a simmer, cover, and cook until the potatoes are tender. If using, add the browned sausage slices back to the pot. Continue to cook until just heated through.
In a small pan, drizzle the remaining 2 tablespoons oil over medium heat. Whisk in the flour until smooth and cook until golden and bubbly. Remove from heat and stir in the paprika. Stir into the soup.
Transfer the soup to individual bowls, season as desired with white vinegar, top with parsley and sour cream, and serve with slices of rustic bread.