The Best Chicken and Dumplings

For the chicken:
1 tbsp. vegetable oil
2 ½ pounds chicken (split breasts, thighs and drumsticks), rinsed and pat dry
2 cup flour
½ teaspoon salt
½ teaspoon freshly cracked pepper

For the broth:
1 cup diced carrot
2 stalks celery, diced
1 large onion, diced
3 cloves garlic, smashed then minced
1/4 cup flour
6 cups chicken stock
1/2 cup dry white wine or apple cider
2 teaspoons sugar
2 bay leaves
5 peppercorns
1/2 cup heavy cream
2 teaspoons parsley, chopped
2 teaspoons fresh thyme, chopped
salt/pepper to taste

For the Dumplings:
2 cups cake flour (or all purpose flour)
1 tablespoon baking powder
1 teaspoon salt
2 tablespoons butter, melted
1- 1 1/4 cups milk