Begin by peeling and dicing the Yukon Gold potatoes into uniform chunks for even cooking.
In a large pot or Dutch oven, heat olive oil over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes.
Stir in the minced garlic and cook for an additional minute, being careful not to burn it.
Add the diced potatoes to the pot and stir well to combine with the onions and garlic.
Pour in the chicken or vegetable broth, then add the paprika, salt, black pepper, and thyme. Stir to incorporate all the flavors.
Bring the mixture to a boil, then reduce the heat to low and cover the pot. Let simmer for about 20 minutes, or until the potatoes are fork-tender.
Once the potatoes are tender, remove the lid and stir in the heavy cream. Allow the mixture to simmer uncovered for another 5 minutes, letting the sauce thicken slightly.
Taste and adjust seasoning if necessary. Remove from heat and let sit for a couple of minutes before serving.
Garnish with freshly chopped parsley, if desired, before serving.