Melt unsalted butter over medium heat in a saucepan. When melted, add all-purpose flour, then whisk until the flour is a light golden brown. Bring to a simmer, then continue to cook and whisk. Reduce the heat to low, add thyme sprigs and smashed garlic cloves, then cook until thick.
Add the shredded Brussels sprouts to the greased cast-iron skillet. Remove the thyme sprigs and smashed garlic cloves from the sauce, then pour the béchamel on top. Give it a really good stir.
In a small bowl, combine panko breadcrumbs, remaining shredded Gruyere, grated Parmesan, grated garlic, and extra virgin olive oil. Stir well, then evenly distribute on top of the Brussels sprouts.
Cover tightly with foil, then transfer to an oven and cook. Remove the foil, then cook until the cheese is golden brown and bubbly on top. Cool slightly, then serve!