Preheat oven to 375 degrees. Line a 12-cup muffin tin with paper liners and grease with oil or non-stick spray oil. Or use a silicone muffin pan and grease with oil or non-stick spray oil. See more detailed suggestions in post above.
Bring a large pot of salted water to a boil. Break spaghetti into thirds a little at a time then add to the pot. Cook until “al dente” (just cooked through but not too soft) then drain and rinse with cold water.
Place drained spaghetti in a large bowl. At this point, kids can use clean siccors to cut the spaghetti into smaller peices if you'd like. Not essential, but fun! Add eggs, marinara sauce, spinach, grated carrot, and ½ cup cheese. Season with salt and pepper. Mix with tongs or a large fork until all ingredients are well combined.
Fill prepared muffin tin with the spaghetti mixture. Press the top of each filled cup down gently then sprinkle each cup with a little of the remaining cheese.
Bake until golden brown around the edges, about 13 to 15 minutes. Set aside until cool enough to handle. Serve warm.