Pat chicken completely dry with paper towels, then season both sides generously with salt, pepper, and a pinch of smoked paprika. Cut into 1-inch cubes (or leave whole for shredding later) and set aside.
Heat 1 tablespoon each of olive oil and butter in your Dutch oven over medium-high heat. Add chicken and cook 4–5 minutes, turning occasionally, until golden brown on all sides. Remove to a plate and set aside, leaving the fat in the pot.
Reduce heat to medium and add the remaining butter and olive oil. Add diced onion, carrots, and celery and sauté for 6–8 minutes until softened, then add garlic and cook 30–60 seconds until fragrant.
Sprinkle flour evenly over the vegetables and stir constantly for 3–4 minutes until the mixture turns light golden and smells nutty, scraping the bottom to prevent sticking.
Pour in the white wine and scrape up any browned bits from the bottom of the pot. Simmer for 2–3 minutes until reduced by half and the alcohol smell has cooked off. (Skip if not using wine.)
Slowly pour in chicken broth while whisking continuously, then add chicken bouillon, thyme, dill, bay leaf, and smoked paprika. Bring to a boil, then reduce to a gentle simmer for 5 minutes.
Return browned chicken and any accumulated juices to the pot along with the diced potatoes. Simmer uncovered for 20–25 minutes, stirring occasionally, until potatoes are fork-tender and chicken reaches 165°F (74°C).
Reduce heat to low and slowly stir in the heavy cream, then add the frozen vegetables. Simmer gently for 5 minutes, taste and adjust seasoning, then remove the bay leaf.
Ladle soup into bowls, garnish with freshly chopped parsley and a crack of black pepper, and serve immediately with crusty bread or crackers.