Mashed Potatoes with Ham with refried

2 lbs thin-skinned potatoes , like Yukon Golds, scrubbed but not peeled, sliced 1/4-inch thick 3 large garlic cloves 1 1/2 cups corn kernels (fresh or frozen)[...]

3 tablespoons fresh cilantro , finely chopped 2 tablespoons shallots , finely chopped 2 tablespoons butter , softened 4 teaspoons fresh lime juice 1 1/2[...]