Heat olive oil in a large pot or dutch oven over medium heat. Add garlic and onions. Cook for 3-4 minutes until onions turn translucent and golden. Transfer to a small bowl and set aside.
In the same pot or dutch oven, melt butter. Sprinkle in flour and whisk until smooth and bubbly, about 2 minutes.
Pour in chicken broth, heavy cream, and milk. Whisk together. Add back the onion and garlic mixture, along with broccoli, carrots, mustard powder, smoked paprika, nutmeg, and cayenne. Whisk again, reduce heat to low, cover, and let simmer for 15-20 minutes until broccoli and carrots are tender.
Remove the lid and add shredded cheddar cheese. Mix well. Then season with black pepper and salt to taste. Stir until combined.
Pour into bowls and serve with crispy bread for dipping!
Now, enjoy the cozy warmth and deliciousness of homemade Panera-style soup right at your own table!