Turn off the heat. Use an immersion blender to blend the soup until completely smooth, about 2 minutes. If you like a little texture, blend most of it smooth, then leave a cup or so slightly chunky.
Stir in the heavy cream. Turn the heat back on to low. You want the soup steaming, not boiling. Boiling can make dairy separate and can turn melted cheese grainy.
Add the cream cheese and stir until fully melted, about 2 minutes. This creates a stable, creamy base that helps the cheddar melt smoothly.
Add the grated cheddar a handful at a time, stirring constantly and letting each addition melt before adding the next, about 4 minutes total. If the soup looks too thick, thin it with 1/4 cup broth or water at a time until it's the consistency you like.
Finish with hot sauce (if using). Taste and adjust: more salt for overall flavor, more pepper for a bolder bite, or an extra teaspoon Dijon if you want the cheddar to taste sharper without adding more cheese.