In a big soup pot, heat the oil over medium high heat. Add the onion and most of the hot dogs (reserve about ½ cup of the hot dogs for garnish). Cook, stirring, until the onion is translucent, 7 to 9 minutes.
Add the carrots, celery, garlic, 1 tablespoon salt, and 1 teaspoon pepper and cook, stirring, until the carrots soften slightly, about 8 minutes.
Add the split peas, bay leaf, and 9 cups water and bring to a boil. Reduce the heat and simmer until the split peas break up and become creamy, 50–55 minutes. Season to taste with salt and pepper.
Meanwhile, throw the reserved hot dogs in a small dry skillet over medium-high heat and let them crisp up and get charred, shaking the skillet once in a while, 5 to 6 minutes. Serve the soup garnished with crispy hot dogs and the croutons.
In a medium skillet, melt the butter over medium heat. Add the diced buns and cook, stirring, until golden and the edges are crisped, 5 to 6 minutes. Transfer to a plate and season to taste with salt and pepper.
