Heat the olive oil in a large skillet over medium heat.
Add the sliced smoked sausage and cook until browned, about 5-7 minutes. Remove the sausage from the skillet and set aside.
In the same skillet, add the chopped onion and diced potatoes. Cook for about 10 minutes, stirring occasionally, until the potatoes start to soften.
Stir in the minced garlic, smoked paprika, dried thyme, salt, and black pepper. Cook for an additional 2 minutes until the garlic is fragrant.
Pour in the chicken broth or water, and return the browned sausage to the skillet. Stir to combine all ingredients.
Cover the skillet and reduce the heat to low. Simmer for 15-20 minutes, or until the potatoes are fork-tender and cooked through.
If desired, remove the lid and let it cook for an additional 5 minutes to thicken the sauce.
Remove from heat and garnish with chopped parsley before serving.