Melt butter in a large pot on medium-low heat. Add garlic, onion, and celery sauté until translucent – 2-3 minutes.
Whisk in flour to make roux. Once roux is blonde (off-white), whisk in (or use immersion blender) whole and evaporated milk. Continue to whisk until desired thickness is reached. Season with kosher salt and cracked black pepper.
Add chicken stock, whisking thoroughly. Do not bring to a boil. Season with kosher salt, cracked black pepper, paprika, and mustard powder.
Add broccoli, and carrots, allowing soup to simmer 15-20 minutes; stirring occasionally.
Puree soup with an immersion blender to desired consistency. Slowly mix in shredded cheddar cheese until thoroughly incorporated.