Preheat the oven to 180°C (350°F).
In a medium saucepan, melt the butter over medium heat. Add the flour and whisk continuously for 2-3 minutes to make a roux.
Slowly pour in the milk while whisking constantly to avoid any lumps. Cook until the mixture thickens, then remove from heat.
Stir in the Dijon mustard and season with salt and pepper to taste.
In a greased baking dish, arrange a layer of potato slices, followed by a layer of grated Gruyère cheese. Repeat this layering process until all the potatoes and cheese are used.
Pour the milk mixture over the potato and cheese layers, ensuring it covers them completely.
Cover the baking dish with aluminum foil and bake in the preheated oven for 40 minutes.
Remove the foil and bake for an additional 10-15 minutes or until the top is golden and bubbly.
Once cooked, garnish with fresh chives and serve hot.