Place the potatoes in a large pot filled with water and a pinch of salt. Bring to a boil over high flame until the potatoes are cooked through and easily pierced with a fork, about 25 minutes.
Strain the morels, reserving 3 Tbsp. of the soaking liquid.
When the potatoes are cooked, gently mash them together with the corn, garlic, 1 Tbsp. butter or oil and soaking liquid until combined. Season with salt and pepper, to taste, and spoon evenly into the morels. Heat 1 Tbsp. of oil in a pan over medium flame and add the morels. Cook, flipping once, until they just turn brown and crispy. Divide among 2 plates.