Preheat oven to 375. Add cream cheese and milk to a blender. Blend until smooth. Set aside.
Peel turnips and slice very thinly. (Mandolin or food processor works best.)
Heat large oven-proof skillet over medium-low heat. Add 2 tablespoons butter. When butter is melted, arrange turnips in a single layer over the melted butter. Top with an additional 1 Tbsp butter and 1 teaspoon garlic. Pour 2 tablespoons broth over turnips. Pour 1/2 cup cream cheese mixture over the turnips. Add 1/3 the cheese over the turnips.
Repeat layers two more times: 1 layer of turnips, 1 tablespoon butter, 1 teaspoon garlic, 2 tablespoons broth, 1/2 cup cream cheese mixture, 1/3 the cheese.
Bake, uncovered, 20-25 minutes or until turnips are tender and dish is bubbly and browned on top.