Add the potatoes to a large pot. Bring to a boil. When they're cooked through, the fork should easily slide into the potatoes with no resistance. The potatoes should almost, but not totally, fall apart.
Drain the potatoes in a large colander. Peel the potatoes and place them back in the pot. Mash the potatoes before adding in all the other ingredients.
In a cast iron skillet, melt butter, add shallots and cook until translucent. Add garlic and stir until fragrant about 30 seconds. Add cream and stir until combined with butter and warmed through.
Add cream mixture to the mashed potatoes and yams. Stir to combine.