Preheat oven to 350℉ in prep for baking later.
(If using already grated cheese, skip this and begin melting butter. However, if grating your own cheese I recommend grating cheese before melting butter to avoid burning your milk mixture while trying to grate your cheese quickly.)
Melt butter over medium heat in a large sauté pan.
Once melted, add shallots and cook for 3 minutes or until soft.
Add flour and mix until combined.
Whisk in milk slowly and bring mixture to a boil being sure to whisk constantly.
Add heavy cream, dijon mustard, salt and pepper, and cheddar cheese and mix until combined.
Then add gruyère cheese and stir until all the cheese is melted and then remove pan from heat.