Heat 2 teaspoons of the oil in a large saucepan over medium heat. Add the bacon, onions, garlic and carrot. Cook, stirring often, until softened and lightly browned, 3 to 5 minutes. Add stock, split peas, thyme, cayenne and bay leaf. Bring to a simmer. Reduce the heat to medium-low, cover, and cook until split peas have broken down and thickened the soup, about 1 hour.
Meanwhile, preheat the oven to 180°C. Cut bread into cubes and toss with the remaining oil in a medium bowl. Spread on a small baking pan and bake until crisp, 15 to 20 minutes.
When soup is ready, discard the bay leaf. Garnish each serving with croutons. The soup will keep, covered, in the refrigerator, for up to 2 days. Keep croutons separate in a sealed container.