Season chicken liberally with salt, pepper and smoked paprika on both sides.
In a large Dutch oven or pot with a lid, head two tablespoons of oil over medium high heat. Add chicken in one layer (do not overcrowd the pan, you may need to do this in batches) and sauté until browned and not sticking to the pan. Flip and brown the other side, about 6-8 minutes total. Transfer to a plate.
Add 2 tablespoons oil to the pot, heat, and add shallots, carrots and leeks. Cook until browned, stirring regularly, about 6 minutes. Add garlic and sauté for 1 more minute.
Add wine, broth and thyme to the pot. Bring to a simmer while stirring and releasing the browned bits stuck to the bottom of the pot. Then add in chicken, potatoes and tomatoes. Bring back to a simmer, lower heat to medium low, and cover.
Braise until chicken is cooked and tender and potatoes are fork tender, about 40 minutes.
Remove chicken, potatoes and vegetables with a slotted spoon onto a platter. Cover with foil to keep hot. Remove thyme.
You can serve the sauce as is or thicken it if desired. To thicken sauce, mix 1 tablespoon cornstarch with 1 tablespoon water to form a paste.
Add paste to the sauce and cook for 2-3 minutes until sauce thickens to coat a back of a spoon and you can't taste the cornstarch.
Season with salt and pepper to taste if needed.
Pour sauce over chicken or serve on the side and garnish with parsley!