Preheat oven to 375 degrees. Make the bechamel: Melt butter in a saucepan over medium heat. Add flour and whisk until mixture bubbles slightly but has not started to brown, about 2 minutes. Gradually whisk in milk. Raise heat to medium-high and bring to a boil, whisking often. Reduce heat to low and cook, stirring occasionally with a wooden spoon, until thickened, 12 to 15 minutes. Season with coarse salt and pepper. Remove from heat. Add smoked Gouda and stir until melted.
Meanwhile, blanch the brussels sprouts: Bring a medium pot of salted water to a boil. Cook brussels sprouts until just tender when pierced with the tip of a paring knife, 3 to 4 minutes. Drain and transfer to an 8-cup (8-by-12-inch) baking dish.
Assemble the gratin: Pour bechamel over brussels sprouts and sprinkle with aged Gouda and a pinch of smoked sea salt. Bake, uncovered, until bubbling and golden, about 25 minutes.
Bechamel can be refrigerated for up to 4 days. Cooled blanched brussels sprouts can be refrigerated for up to 1 day. Assembled gratin can be refrigerated overnight. Bring to room temperature before baking.
Also I would recommend slicing the brussel sprouts in half so they are easier to eat
Blanching brussels sprouts still has that awful bitter taste no one enjoys. Roasting the brussel sprouts would have made for a tastier dish, though the sauce came out well.