Start by washing and chopping your broccoli into bite-sized florets. Dice the onion finely and mince the garlic cloves.
Heat the olive oil in a large pot over medium heat. Add the diced onion and cook until translucent, about 4-5 minutes. Stir in the minced garlic and cook for another 1-2 minutes until fragrant, being careful not to let it burn.
Sprinkle the all-purpose flour over the onion and garlic mixture. Stir constantly for 2-3 minutes to cook out the raw flour taste and create a roux that will thicken your soup.
Slowly whisk in the chicken broth, ensuring no lumps form. Add the chopped broccoli and bring the mixture to a simmer. Cook for about 10-12 minutes, or until the broccoli is tender.
If you prefer a smoother texture, carefully transfer half of the soup to a blender and puree until smooth, then stir it back into the pot. This step is optional but recommended for a creamy consistency without losing the broccoli's body.
Lower the heat and stir in the heavy cream. Gradually add the shredded cheddar cheese, stirring continuously until the cheese melts completely. Season with salt and pepper to taste. Keep the soup on low heat to avoid curdling.
While the soup is finishing, take your bread bowls and carefully cut out the top and hollow out the center, leaving enough bread on the sides to hold the soup without leaking.
Ladle the hot broccoli cheddar soup into each bread bowl. Serve immediately and enjoy the delightful combination of creamy soup and crunchy bread bowl.