Heat a large Dutch oven over medium-high heat with the EVOO, four turns of the pan. Quarter and core the fennel, then chop into a small dice and add to the pot. Chop the vegetables and keep adding to the pot as you work to keep your cutting board clear – add the diced celery, chopped parsnips, carrots, potatoes, onion, garlic, and season liberally with salt and pepper; add in the bay leaves and thyme. Sweat the vegetables for 8-10 minutes covered, stirring fairly frequently, then add the wine and deglaze the pot. Stir in the stock plus 2 cups water and bring to a boil.
Heat the butter in a small skillet over medium heat to melt, then whisk in the flour for 1 minute. Scrape the roux into the soup. Simmer the soup for a few minutes to combine the flavors, then cool and cover for a make-ahead meal.
Bring the soup to a boil over medium to medium-high heat, stirring occasionally. Stir together the biscuit mix with water and parsley, according to the package directions. When the soup comes to a boil, add in the peas, dill and reserved fennel fronds. Using two spoons, drop the biscuit mix into a pot, shaping small egg-shaped dumplings as you go. Cover and simmer over medium-low heat for 10 minutes. Turn off the heat and serve the hearty, thick soup in shallow bowls.