To make the sauce, heat olive oil in a small pot over medium-high heat and saute the chopped onion, carrots, and garlic for a few minutes until slightly softened. Add red pepper flakes, crushed tomatoes, oregano, and basil, and stir to combine. Cover and bring just to a boil, then reduce heat to low and simmer 20 minutes, stirring occasionally to prevent the bottom from burning. Remove from heat and let cool slightly, then blend well with an immersion stick blender. (Do ahead: sauce can be made up to a week ahead of time. Reheat before continuing.)

Spoon 1/4 cup of warm sauce into each of 8 ramekins (use leftover sauce for another use), then dot each ramekin with about 2 teaspoons crumbled goat cheese. (Do ahead: ramekins can be prepared with sauce and cheese the day before, then covered and refrigerated overnight. Heat in the preheating oven until ramekins and sauce are warm, not hot, and continue with the recipe.)

Crack an egg into each ramekin, sprinkle with salt, and bake in a preheated oven at 425F for 15-20 minutes, until whites have set but yolk is still soft.

Garnish with fresh basil chiffonade, if desired, and serve immediately with toast points for dipping into the yolk and sauce.