Begin by preparing the vegetables. Dice the onions, slice the carrot into rounds, and chop the broccoli into pieces, keeping the stalk if you like. Just make sure everything is well washed.
In a deep pot, heat olive oil and sauté the onions for a few minutes over medium-high heat until caramelized.
In a separate pot, heat the water you'll use for the soup to save time.
Add the carrots to the onions and sauté for a few more minutes, stirring occasionally. Add a splash of water if needed.
After a few minutes, add the broccoli and pour in the hot water. Season with salt and pepper, and let it cook for about 25 minutes, or until all the vegetables are soft.
Meanwhile, make a béchamel-like sauce. Heat olive oil in a small pot, then stir in the flour. Cook for about 2 minutes, whisking constantly.
Pour 1 cup of water from the soup into the béchamel, whisking until thickened.
Add the thickened sauce to the soup about 3 minutes before it’s finished cooking.
Remove the pot from the heat and blend the soup until smooth using a hand blender. If you don’t have one, let the soup cool slightly before blending in a regular blender.
Serve with croutons or your favorite toppings, and enjoy!