Peel the potatoes and cut them into thin slices (1/8-inch thick) or use a mandoline to ensure they are all even. Use a 1 1/2-inch round cookie cutter to cut out rounds from the yellow and sweet potatoes (the blue potatoes should already be the right size). Cook the potatoes separately in boiling water for 2 minutes, leaving the blue potatoes for last; remove them and dry them. Cut the cheese into very thin slices and use the cookie cutter to obtain rounds the same size as the potatoes. Arrange the potatoes by alternating the colors and the cheese slices, forming concentric rings, until you fill up a round 9- or 10-inch baking dish. Season with salt and a drizzle of oil and bake at 350°F for 45 minutes. Remove from the oven and top with thyme leaves and chopped walnuts.