Fill a large pot with 8 cups of water and place on stove top. Do not turn on yet.
Peel and chop potatoes in 1 inch cubes.
Add the potatoes to the pot of water. Turn stove on high to bring to a boil.
Once boiling, turn stove down to a simmer and cook for 2 minutes before adding the cauliflower.
After adding cauliflower continue boiling for 10 minutes. Cauliflower and potatoes will be fork tender.
Drain the vegetables and return to the pot. Add the butter, salt, and pepper and mix with a hand mixer or potato masher. Stir in goat cheese and thyme.
Use a spatula to scrape the mash into serving bowl. Garnish with additional thyme leaves and a pat of butter.
Store leftovers in an airtight container for 2-3 days.