Preheat the oven to 425 degrees F. I suggest using a shallow oven safe dish such as a dutch oven.
Melt 1 tablespoon of butter over a medium low heat. Add in the 1 pound of trimmed and sliced Brussels sprouts, and sauté until bright and seared. About 5 minutes.
Set Brussels sprouts aside.
Using the same dish, melt 1 tablespoon of butter. Add ¼ cup shallots, 1 tablespoon minced jalapeño, 2 cloves of minced garlic, and sauté for 1 minute, until aromatic.
Add 1 tablespoon flour and mix until all of the shallots, jalapenos, and garlic are covered.
Add the ½ cup vegetable broth, ½ cup milk, and ½ cup cream. You can use whipping cream or half and half.
Bring the mixture to a low simmer, careful not to boil, and cook until liquid begins to thicken. Cook for about 2 minutes. Turn off heat.
Turn off heat.
In small batches, add in ½ cup gruyere and ¼ cup cheddar. Fully mix in the cheese before adding more. Repeat until all of the cheese is added and incorporated.
Fold in seared brussel sprouts.
Melt the remaining 1 tablespoon of butter. Mix the melted butter with ¼ cup panko breadcrumbs and some of each cheese.
Top the cheesy Brussels sprouts with the breadcrumb mixture. Transfer the dish to the oven and bake at 425 for about 20 minutes, until the sauce is bubbly and the breadcrumbs are golden.
Broil on low for a few minutes for toastier breadcrumbs.