Cut chicken breasts into 1/2-inch cubes and season them with 3/4 tsp salt, 3/4 tsp garlic powder, and 3/4 tsp onion powder, stirring to coat evenly. While the chicken seasons, finely dice the white onion into 1/4-inch pieces, cut broccoli into small bite-sized florets, shred the carrots on a large-hole grater, and grate the cheddar cheese. Having everything prepped and ready will keep the cooking process smooth and prevent overcooking any component.

Heat 1 tbsp olive oil in a large pot or Dutch oven over medium-high heat until shimmering. Add the seasoned chicken cubes and cook for 5-7 minutes, stirring occasionally, until golden on the outside and cooked through to an internal temperature of 165°F. Transfer the cooked chicken to a clean plate and set aside—I like to keep the flavorful browned bits in the pot as they'll add depth to the broth.

In the same pot with the chicken drippings, melt 1 tbsp of the remaining butter over medium heat. Add the diced onions and sauté for 2-3 minutes until softened and fragrant, stirring occasionally. Then add the remaining 4 tbsp butter and let it melt completely, whisk in the flour, and cook for 1 minute, stirring constantly to create a light-colored roux. This roux will thicken the soup and provide a subtle toasted flavor that balances the creaminess.

Slowly pour in the chicken broth while whisking constantly to prevent lumps from forming in the roux. Once fully incorporated, add the cream (at room temperature to prevent curdling) and whisk until smooth. Bring the mixture to a gentle simmer and cook for 2 minutes, whisking occasionally, until the sauce thickens slightly and becomes silky.

Stir in the broccoli florets, shredded carrots, and all remaining seasonings: 1 1/4 tsp salt, 1/2 tsp paprika, 1/2 tsp garlic powder, 1/4 tsp mustard powder, 1/4 tsp cayenne pepper, and 1/4 tsp fresh ground black pepper. Reduce heat to medium and simmer for 10-12 minutes until the broccoli is tender but still vibrant green and the carrots are just softened. The vegetables release their natural flavors into the broth, creating a well-rounded taste.

Using an immersion blender, blend the soup to your preferred consistency—I like to blend about half the soup for a chunky-smooth texture that still has texture from the vegetables. Alternatively, transfer half the soup to a regular blender, purée, and return it to the pot. Reduce heat to low and stir in the grated cheddar cheese until completely melted and fully incorporated, which should take about 2-3 minutes of gentle stirring.

Gently fold the cooked chicken from Step 2 back into the pot and stir until evenly distributed and heated through, about 1-2 minutes. Taste and adjust seasonings as needed. Ladle into bowls and serve hot—this soup is best enjoyed immediately while the cheddar is silky and the broccoli is at its peak texture.