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Step 1
Zest the lemon, set zest aside.
Step 2
Prep the artichokes. Fill a med bowl with 4 cups cold water and squeeze with the juice from the lemon. Because artichokes will easily brown, work on one at a time as quickly as possible. Snap off all the hard out leaves using your fingers ( Save for later) With a sharp paring knife, trim off all the outer green skin around the base and stem, keeping the stem in tact. Remove the yellowish soft leaves and using a spoon, gently scrape away the white or purple silk like threads. Immediately place in the lemon water, to prevent browning. Slice just before placing in the skillet.
Step 3
Preheat oven to 425F. Pat chicken dry and season with kosher salt and pepper. Heat 1 T butter and 1 T olive oil in a heavy bottom oven proof skillet over med high heat. Place chicken skin side down and sear for until golden, about 5 minutes. Turn and brown undersides until golden, about 7-8 minutes. Remove chicken and set aside. Drain some of the chicken fat, leaving about 1 tablespoon oil in the pan. Add 1 tablespoon more butter. Add leeks, sliced artichokes, sliced potatoes and fennel seeds. Saute on med heat for 8-10 minutes, stirring frequently, until they just begin to soften. Season with a generous pinch of kosher salt and pepper.
Step 4
Deglaze the pan with vermouth (or white wine). Reduce by half, about 4 minutes. Add stock, mustard and fennel seeds, half and half, half of the fresh tarragon and 1/2 of the zest. Give a stir, bring to a simmer, and taste broth adjusting salt and pepper. Nestle the chicken pieces into the stew with skin sides up, and roast in a hot 425 F oven for 20-30 minutes, until golden, and thigh internal temp is 170F, or breast internal temp is 160F. If needed, broil for a couple minutes to get skin extra crispy.
Step 5
Garnish with remaining lemon zest and fresh tarragon before serving.