Combine lemon juice and cream in a small bowl. Season with 1/4 teaspoon salt. Mash 1 teaspoon flour and 1 teaspoon butter in another small bowl until a paste forms. Set both bowls aside.
Dry chicken thoroughly with paper towels. Season with the remaining 1/4 teaspoon salt and white pepper. Dredge lightly in the remaining 1/2 cup flour, shaking off any excess. (Discard leftover flour.)
Heat the remaining 1 tablespoon butter and oil in a 12-inch cast-iron skillet over medium-high heat. Add the chicken—do not crowd the pan. Cook, turning once, until nicely browned on both sides, about 10 minutes total. Add 1/2 cup broth, reduce the heat and cover. Simmer until the chicken is cooked through, 4 to 6 minutes. (Check to make sure the pan juices don’t run dry. If necessary, add more broth, a tablespoonful at a time, to prevent scorching.) Transfer the chicken to a clean cutting board and tent with foil.
Add the remaining 1/2 cup broth to the pan and bring to a boil over high heat. Cook until reduced to about 1/4 cup, 2 to 4 minutes. Reduce heat to medium, add the reserved lemon cream and bring to a simmer. Gradually whisk in the reserved butter-flour paste, a few bits at a time, until the sauce coats the spoon, 1 to 2 minutes. Stir in peas.
Reduce the heat to low and return the chicken to the pan along with tarragon (or dill). Turn to coat with the sauce and cook until heated through, 1 to 2 minutes. Slice the chicken and serve with the sauce, garnished with sprigs of tarragon (or dill), if desired.
