In a soup pot, melt butter.
In melted butter saute diced yellow onions and minced garlic. Saute for 2 minutes until onions begins to sweat.
To make roux (to thicken the soup) add all-purpose flour(for gluten free option use gluten-free all purpose flour). Using a whisk, mix flour in butter and cook on low flame for about 2 minutes. Do not stop whisking.
Pour chicken stock gradually while whisking flour and cooking it.
Add the half n half as well. Continue to whisk and cook for 3 to 3 minutes.
Add in diced carrots and finely chopped broccoli. Use grated carrots and chop broccoli fine if you don’t want to blend this soup and if you like to leave it chunky.
Add in all the spice powders. Freshly ground pepper, ground mustard, cayenne pepper, paprika and nutmeg(I skipped nutmeg) to the soup pot. Mix well until combined.
Cover soup pot with lid and let it simmer for 15 minutes on low flame until broccoli and carrots are cooked and tender.
If you want to have smooth creamy soup, blend it with immersion blender. Skip blending if you like chunky soup.
Blend soup. If you liked smooth creamy soup, blend for few extra seconds. Or you want to leave some chunks do not blend all the way.
Turn off flame. Add cheese in 3-4 parts.
Cook’s Tip : Make sure heat is off before you start adding cheese to the soup and stir until all cheese melts. Add the next portion of cheese only after the first batch of cheese is completely melted. This will prevent cheese turning grainy.
Once all cheese is added to soup pot and it’s melted, serve immediately hot in bread bowl and in regular soup bowl with crusty bread to dunk.
Garnish with steamed broccoli florets and extra cheddar cheese on top before serving.