Melt butter in a Dutch oven over medium-high heat; add onion, and sauté 5 to 6 minutes or until tender. Add garlic and red pepper, and cook 2 minutes. Stir in chicken broth and broccoli. Cover and bring to a boil; reduce heat to medium, and cook 10 to 15 minutes or until broccoli is tender. Stir in cream cheese.
Process mixture with a handheld blender until smooth. Add chicken and shredded cheese. Cook, stirring occasionally, 5 minutes or until cheese is melted. Season with salt and pepper to taste. Serve immediately with almonds, if desired.
Note: If you don't have a handheld immersion blender, let mixture cool slightly; process mixture, in batches, in a regular blender until smooth, stopping to scrape down sides as needed. Return mixture to Dutch oven, and proceed as directed.