Add the broccoli florets, diced onion, minced garlic, and one diced jalapeño to the slow cooker.
In a small bowl whisk the flour into the vegetable broth until smooth, then pour the mixture into the slow cooker.
Stir in the salt and black pepper.
Cover and cook on low for 6 hours until the broccoli is very soft.
Use an immersion blender to puree the soup until mostly smooth with a few small pieces remaining.
Stir in the milk, then gradually add the shredded cheddar cheese until fully melted.
Taste and add the remaining diced jalapeño if more heat is desired.