In a large cast-iron or other heavy skillet, heat the butter over low heat. Add sweet potatoes, garlic, 1/4 teaspoon salt and thyme; cook, covered, until potatoes are almost tender, 4-5 minutes, stirring occasionally. Stir in spinach just until wilted, 2-3 minutes., With the back of a spoon, make 4 wells in potato mixture. Break an egg into each well. Sprinkle eggs with pepper and remaining salt. Cook, covered, on medium-low until egg whites are completely set and yolks begin to thicken but are not hard, 5-7 minutes.