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1
Heat the oil in a large, heavy-bottomed pot or Dutch oven over medium-high heat until shimmering. While the pot is heating, pat the chicken very dry with paper towels, and then generously season with salt and pepper.
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2
Place half of the chicken in the pot and sear until golden-brown on the bottom, 5 to 6 minutes. Remove to a large plate and repeat with the remaining chicken (only sear on one side; the chicken will not be cooked through). While the chicken is searing, quarter the potatoes and set aside. Cut the radishes in half and set the leafy tops aside.
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3
After the chicken is seared, reduce the heat to medium and add the onion and thyme. Season with salt and pepper and cook, stirring occasionally, until the onion is softened, about 5 minutes. Add the flour, stir to combine, and cook out the floury taste, about 1 minute.
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4
Add the broth and 3/4 teaspoon salt and stir with a wooden spoon to fully dissolve the flour in the broth and scrape up any browned bits at the bottom of the pan. Add the potatoes and radishes (save the tops for later), stir to combine, and bring to a full boil. Add the chicken and any accumulated juices on the plate, nestling the chicken into the vegetables.
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5
Cover, reduce the heat to medium-low, and simmer, stirring every 5 minutes, until the vegetables are tender and the chicken is cooked through, about 15 minutes total. Transfer the chicken to a serving platter.
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6
Add the radish tops and peas to the pot, stir to combine, and simmer uncovered until just cooked through, about 2 minutes. Remove from the heat, add the parsley and lemon zest, and stir to combine. Taste and season with salt as needed. Serve the braised vegetables with the chicken.
