Start by slicing your yellow onions thinly. Heat 2 tablespoons of olive oil in a large heavy-bottomed pot over medium-low heat. Add the onions along with a pinch of salt, and cook slowly, stirring occasionally, for about 30-40 minutes until they turn deep golden brown and smell sweet and rich.
Preheat your oven to 200°C (400°F). Toss chopped carrots, celery, and bell pepper with a tablespoon of olive oil, a pinch of salt, and pepper. Spread them out evenly on a baking sheet and roast for 25-30 minutes until tender and slightly charred, adding a smoky depth to their flavor.
Once the onions are deeply caramelized and fragrant, add the sprigs of thyme and bay leaf to the pot. Pour in 4 cups of vegetable broth and bring to a gentle simmer. Let it cook for about 10 minutes to allow the flavors to meld, then remove the thyme sprigs and bay leaf.
Add the roasted vegetables to the broth in the pot. Use an immersion blender to purée the soup directly in the pot until smooth and velvety, or carefully transfer in batches to a blender and blend until creamy. If the soup is too thick, stir in a little more broth; if it's too thin, simmer gently to thicken.
Taste the soup and adjust the seasoning with salt and pepper. For an extra umami boost, stir in a splash of soy sauce or miso if desired. Remove from heat and let sit for 5 minutes to deepen the flavors.
Ladle the soup into bowls. If you like, drizzle with balsamic glaze or sprinkle with grated cheese for added richness. Serve hot with crusty bread on the side for a complete, comforting meal.