Bring water to a boil in a large pot and cook the spaghetti according to the package instructions. Drain and set aside.
In a separate pan, heat the olive oil over medium heat. Add the onions, bell pepper, garlic, and sauté until softened.
Add the grated carrot, thyme, and parsley to the pan, and cook for another 2-3 minutes.
Stir in the tomato paste and cook for a few minutes, allowing the flavours to meld together.
add the sliced hot dogs to the pan and cook for a few minutes to heat them through.
Add the cooked spaghetti to the pan and toss to coat the spaghetti with the vegetable and tomato mixture.
Adjust the seasoning with salt and pepper to taste. If you like it spicy, you can also add a scotch bonnet pepper to the dish for some heat.
Once everything is well combined and heated, the Haitian spaghetti is ready to be served.