Broccoli-Cheddar Soup

I'm currently trying to re-discover my love of cooking...and Cook's Illustrated helped by providing a recipe for "Broccoli-Cheese Soup" in their March/April 2011 issue, from which this version is adapted.

4+ tbsp. unsalted butter
2 pounds broccoli, florets roughly chopped into 1-inch pieces, stems peeled and cut into 1/4-inch thick slices
1 medium onion, coarsely chopped (about 1 cup)
2 medium garlic cloves, minced or pressed (about 2 tsp.)
1 1/2 tsp. dry mustard
pinch cayenne pepper
1 tsp. salt
5-6 cups homemade chicken broth
1/4 tsp. baking soda (optional; see below)
2 ounces baby spinach (2 loosely packed cups)
3-4 ounces sharp cheddar cheese, shredded (3/4-1 cup)
1 1/2 ounces Parmesan cheese, grated fine (about 3/4 cup)
Ground black pepper

Heat butter in large saucepan over medium-high heat. When foaming subsides, add broccoli, onion, garlic, dry mustard, cayenne, and salt. Cook, stirring frequently, until fragrant, about 6 minutes. Add 1 cup broth and baking soda (if desired). Bring to a simmer, cover, and cook until broccoli is very soft, about 20 minutes (if using baking soda) or 1 hour (if not using baking soda). Stir every ten minutes during cooking.

Add 4 more cups of broth and increase heat to medium-high. When mixture begins to simmer, stir in spinach and cook until wilted, about 1 minute. Add cheeses, and process with an immersion blender until smooth.

Adjust consistency with up to 1 cup more of broth, if desired, and season with plenty of salt and pepper to taste.