Preheat the oven to 400°F Lightly grease one 2-qt baking dish (or 6 1-cup ramekins) with olive oil.
To prepare the biscuit dough, whisk the 1 1/4 c flour, baking powder, salt, and parsley in a medium bowl. Cut in the cold butter and work it in with your fingertips or a pastry blender until the mixture resembles soft bread crumbs. Add the milk, stirring just until the dough comes together. Set aside.
Cut the chicken breasts into large bite-size pieces. Toss the pieces in a bowl with the 1/4 c flour and 1 teaspoon each of salt and pepper. Set aside.
Heat 1 tbsp olive oil in a large Dutch oven or sauté pan over medium-high heat. When the oil is shimmering and giving off wisps of smoke, add the chicken and brown for about 6 minutes, turning halfway through. Remove the chicken and set aside.
Reduce the heat to medium. Add the onion, fennel, and garlic. Cook until vegetables soften, about 5 minutes. Add the potatoes and increase the heat up slightly. Cook 3-4 minutes, then add the lemon zest, lemon juice, and wine and bring to a simmer, scraping up any brown fond from the bottom of the pan. Add the peas and carrots, the broth and the chicken, and season the stew with 1 teaspoon of salt and plenty of black pepper to taste.
Spread the stew in the prepared baking dish or ramekins. Drop the biscuit dough on top in 6 to 8 evenly spaced mounds (or drop one generous spoonful on each ramekin) and sprinkle the Parmesan cheese over the top. Bake, uncovered, about 40 minutes, until the chicken is fully cooked and the biscuits are golden.