Heat the olive oil in a large pot over medium-high heat. Add the diced onion and minced garlic, then sauté for about 2 minutes until fragrant and translucent.

Add the broccoli florets, cubed potato, chopped parsley, bay leaf, and vegetable broth to the pot with the sautéed aromatics. Season with salt and freshly ground black pepper to taste. Stir well and bring to a gentle boil.

Lower the heat to a simmer, cover the pot, and let the soup cook for about 15 minutes. The vegetables should become tender and easy to blend.

Remove the bay leaf from the soup and discard it. Carefully blend the remaining mixture using an immersion blender or by transferring to a regular blender in batches, blending until smooth. I like to add a touch more black pepper at the end for a flavor boost before serving.