In a large pot, sauté the diced onion in a splash of broth over medium heat for 5 minutes until softened. Add garlic and cook for 1 minute until fragrant.
Add broccoli florets and chicken broth to the pot. Bring to a boil, then reduce heat and simmer for 12-15 minutes until broccoli is very tender.
Use an immersion blender to puree the soup until mostly smooth, leaving some texture if desired. Stir in almond milk, garlic powder, nutmeg, salt, and pepper.
Remove pot from heat and stir in shredded cheddar cheese and Greek yogurt until melted and smooth. Taste and adjust seasonings before serving warm.