Heat 2 tablespoons of olive oil in a large deep pot or Dutch oven over medium-high heat.
Add the cut chicken pieces and fry on all sides until golden brown, about 3 minutes.
Add the 1/2 diced onion and 3 chopped garlic cloves, cook and stir until tender, about 2 minutes.
Pour in the 1/2 cup of white wine and stir to loosen any bits of food stuck to the bottom of the pot.
Pour in the 1 cup of chicken broth and bring to a boil.
Add the 3 diced carrots and 1 package of frozen green peas, season with 1 teaspoon ground cumin, 1 teaspoon paprika, salt, and pepper.
Reduce heat to low, cover, and simmer for 25 minutes or until the chicken easily pulls away from the bone.
Heat the remaining 1/4 cup of olive oil in a large skillet over medium-high heat.
Fry the 3 large peeled and cubed baking potatoes in the oil, stirring frequently until tender.
Adjust heat as needed to keep the potatoes from burning, remove with a slotted spoon, and drain on paper towels. Season with salt and pepper.
To serve, place a piece of chicken onto each plate, spoon some of the carrots and peas with the cooking liquid over it, and top with a spoonful of fried potatoes.