Heat butter or olive oil in a large skillet or Dutch oven over medium heat.
Add the diced raw chicken, season with a pinch of salt and pepper, and cook for 3–4 minutes until the outside is no longer pink (it does not need to be fully cooked yet).
Add onion, carrots, celery, and diced potatoes. Cook for about 5 minutes, stirring occasionally.
Stir in garlic and cook for 30 seconds until fragrant.
Sprinkle flour over everything and stir well to coat. Cook for 1 minute.
Slowly pour in chicken broth while stirring to prevent lumps. Add milk, poultry seasoning (or thyme), salt, and pepper.
Bring to a gentle simmer. Cover and cook for 10–12 minutes, stirring every few minutes, until: potatoes are fork-tender, chicken is fully cooked, sauce is thick and creamy, and if it thickens too fast, add a splash more broth
Stir in peas (and corn if using) for the last 1–2 minutes.
Taste and adjust seasoning. Add a splash of cream if you want it extra cozy.
Serve warm, topped with biscuit halves or alongside crusty bread.