In a large stockpot, bring the chicken broth to a boil. If the potatoes aren't fully covered by the broth, supplement with water.
While waiting for the broth to boil, peel and rinse the potatoes. Cut them into bite-size pieces. Place the potato pieces in the boiling chicken broth. Once it returns to a boil, reduce the heat to medium-low. Let them simmer until they become soft, roughly 10 to 15 minutes, depending on the size of the potato pieces.
Once done, drain the potatoes. Add the butter, cream cheese, salt, and white pepper to the pot. Either use a hand mixer to whip the mixture until smooth or use a potato masher to integrate the ingredients until the cheese and butter are fully melted.
Finally, stir in the smoked gouda cheese until it melts. Serve the mashed potatoes while they're hot.
Notes
Note: If you're preparing this dish for a large dinner, the mashed potatoes can be kept warm in a slow cooker. Just transfer them to the cooker and set it to low for 1 to 2 hours.