Preheat oven to 425ºF. Butter either a deep dish pie pan or a small baking dish (The dish I used was an 8x11, but an 8x8 also works!)
Season chicken thighs all over with salt and pepper. Heat olive oil in a large pot over medium heat.
Add in chicken thighs, skin side down, and cook until deeply brown, about 8-10 minutes.
Flip and continue to cook, adjusting heat as needed, until the chicken is cooked through, about 10-15 minutes more. Remove chicken and set aside.
Add celery, carrots, onion, fennel and garlic to the same pan with the drippings. Season with salt and pepper. Cook, stirring, until the veggies start to soften, about 5-7 minutes.
Stir in paprika and cook for 1 minute more. Add in butter and melt.
Stir in flour and cook for 1 minute. Whisk in chicken stock and cook, stirring, until the sauce is bubbling and thick. Add in thyme and bay leaf (tied together with twine if you have it).
Reduce heat to low and simmer, stirring often, for 10 minutes.
While sauce simmers, remove skin and bones from chicken and shred.
Once the sauce has simmered, remove thyme and bay leaf. Stir in shredded chicken. Turn off heat.
Add in sour cream, peas, fresh herbs, and lemon zest. Season to taste with salt and pepper.
Pour filling into the prepared dish.
Whisk egg and water together to make an egg wash.
Roll out puff pastry if necessary to fit your dish. If you are using a pie plate, just keep the shape of the pastry square and drape it over the filling. It doesn’t have to fit perfectly, you just want the top to be fully covered.
Brush egg wash all over the crust and sprinkle with flake salt.