Preheat and prep: Heat the oven to 400°F (200°C). Grease a 9x13-inch baking dish or large ovenproof skillet.
Measure and prep all your ingredients so the sauce comes together smoothly.
Cook the veggies: In a large skillet or Dutch oven, heat butter and olive oil over medium heat. Add onion, carrots, and celery with a pinch of salt. Cook 6–8 minutes until softened and lightly golden.
Stir in garlic and cook 30 seconds.
Build the flavor: Add thyme, sage, salt, and pepper. Sprinkle flour over the veggies and stir to coat. Cook 1–2 minutes to remove the raw flour taste.
Make the sauce: Gradually whisk in chicken broth, scraping up any browned bits.
Add milk. Bring to a gentle simmer and cook 3–5 minutes until thick and creamy. It should coat a spoon.
Add the chicken and veggies: Stir in chicken, peas, corn, lemon juice, and parsley.
Taste and adjust seasoning with more salt and pepper if needed. Transfer the mixture to your baking dish if not already in an oven-safe pan.
Make the biscuit dough: In a mixing bowl, whisk flour, baking powder, baking soda, and salt. Cut in the cold butter with a pastry cutter or your fingertips until pea-sized bits form.
Stir in cheddar if using. Pour in buttermilk and gently mix until the dough just comes together. If dry, add 1–2 tablespoons more buttermilk.
Shape the biscuits: Turn the dough onto a lightly floured surface.
Pat into a 3/4-inch thick rectangle. Fold in thirds like a letter, turn, and pat again. Repeat once more for extra flaky layers.
Cut into 9–12 rounds or squares.
Top and bake: Arrange biscuits over the hot filling, leaving small gaps for steam. Brush the tops with melted butter. Bake 20–25 minutes, until the biscuits are golden and cooked through and the filling is bubbling around the edges.
Rest and serve: Let it sit 5–10 minutes before serving.
This helps the sauce set slightly so it scoops cleanly.