Heat the olive oil in a large Dutch oven or heavy bottomed soup pot on medium-low heat.
2 Tbsp. olive oil or butter
Add in the carrots, onions, broccoli & broccoli stems and cook on medium-low to sweat the veggies. This will take ~12-14 minutes. Add the kosher salt about half way through the sweating process.
1 cup matchstick/julienned carrots (1/8th inch size), 1 small yellow onion, diced, 3 cups broccoli (2 cups diced very small, 1 cup leave larger florets), 1 cup broccoli stems, diced small, 1 tsp. kosher salt, plus more to taste
Add the garlic and stir until fragrant ~1 minute. Stir in the flour to coat the veggie and cook for ~1 minute to get rid of the floury taste.
1 1/2 tsp. garlic, minced
Whisk in the broth and half and half gradually. Then add the mustard, sugar, hot sauce, paprika, and turmeric. Stir. Bring to a boil over medium-high heat, then return to a low simmer.
3 cups chicken broth, 2 cups half and half, slightly warmed, 1 Tbsp. Dijon mustard, 1 Tbsp. granulated sugar, 1 tsp. hot sauce, 1 1/2 tsp. paprika, 1/4 tsp. turmeric
Add both cheeses in small handfuls, stirring and allowing it to melt between each addition. Repeat until all cheese is added and it has melted. Low and slow heat ensures the soup doesn't separate and keeps the soup smooth and creamy. (Be sure to stir frequently so the cheese doesn’t stick to the bottom).
8 oz. sharp cheddar cheese, shredded, 6 oz. Velveeta cheese, cut into cubes
Whisk in the cornstarch slurry and simmer until thickened. Taste and adjust seasonings as desired (more hot sauce, salt, add pepper, etc.)
1 1/2 Tbsp. cornstarch + 1 1/2 Tbsp. water
Enjoy in a bowl garnished with more cheese and black pepper or serve in a bread bowl and dive into this goodness!