Step 1Heat the oven to 325 degrees. Butter 4 (6-ounce) custard cups or ramekins.
Step 2Heat 1 tablespoon butter and the oil in a medium saucepan. Add the carrots, garlic, thyme and salt and cook over medium heat, stirring occasionally, for 5 minutes. Add one-half cup water, cover the pan, reduce the meat to medium-low and cook until the carrots are soft, about 15 minutes. Remove from the heat and cool slightly.
Step 3Remove 12 carrot slices and arrange 3 over the bottom of each custard cup or ramekin (you can cut them in half to make them fit). Combine the remaining carrots in a blender with the cream and puree until completely smooth. Season with pepper to taste. Add the egg and egg yolk and process until smooth. Divide among the cups.
Step 4Place the ramekins in a larger baking dish and pour in boiling water to come halfway up the sides. Bake 1 hour. Remove from the oven and let stand 5 minutes. Run a small spatula around the rim of each and turn out each onto plates to serve, sliced-carrots side up.