In a large pot, bring about 5 cups of water to a boil. Place whole carrots into the water, cooking just until they are easily pierced through with a fork. Drain the carrots from the water and cool them at room temperature. Once completely cooled, grate the carrots on the largest side of a cheese grater into a large mixing bowl.
Add grated cheese, pressed garlic, and mayonnaise to the mixing bowl with the grated carrots. Stir to combine.
Slice baguette and tomatoes into thin slices.
Assemble the sandwiches by placing a piece of tomato on the bread, followed by a spoonful of the creamy carrot mixture. Keep refrigerated until you're ready to serve. Enjoy!