Heat the vegetable oil in a large pot over medium-high heat. Add the pork cubes and brown them on all sides for 6 to 8 minutes. Remove the pork to a plate and set aside.

Lower the heat to medium and add the diced onion to the same pot. Cook for 4 minutes until softened. Sprinkle in the 3 tablespoons of flour and stir for 1 minute to form a roux.

Slowly pour in the chicken broth while stirring to avoid lumps. Return the browned pork to the pot along with the thyme, 1 teaspoon salt, and black pepper. Bring to a simmer, then cover and cook for 45 minutes until the pork is tender and the gravy has thickened.

Stir in the frozen sweet peas and let them heat through for 3 minutes.

In a mixing bowl, combine the 1 cup flour, baking powder, and 1/2 teaspoon salt. Stir in the milk and melted butter until a soft dough forms. Drop spoonfuls of dough onto the surface of the simmering stew.

Cover the pot and cook for 12 minutes without lifting the lid so the dumplings steam properly. Serve once the dumplings are cooked through.