Peel the potatoes and cut them into even chunks so they cook at the same rate. Place them in a large pot with the garlic cloves and cover with cold water. Add salt to the water for well-seasoned potatoes from the inside out.
Bring the pot to a boil and cook until the potatoes are fork-tender, about 15–18 minutes. They should break apart easily without falling completely apart. Drain thoroughly to avoid watery mashed potatoes.
While the potatoes cook, gently warm the butter, milk, and cream together. This step helps everything blend smoothly and prevents the potatoes from cooling down too quickly.
Return the drained potatoes to the pot and mash them gently. Avoid over-mashing, which can make them gluey. The goal is fluffy with a few soft ridges.
Pour in the warm butter mixture and sprinkle in the smoked gouda gradually. Stir gently until everything melts and combines into a creamy mash.
Taste and adjust salt and pepper as needed. The smoked gouda already adds depth, so season carefully. Serve warm with optional chives on top.