Preheat your oven to 375°F and lightly grease a 9×13-inch baking dish.
Prepare the potatoes by slicing them into ⅛-inch rounds, keeping the slices as uniform as possible so they cook evenly.
In a medium pan over medium-low heat, melt the butter. Add the onion and sauté for 2–3 minutes, just until translucent.
Add the flour and whisk continuously for 1 minute, until fully incorporated into the butter.
Slowly pour in the milk, whisking continuously until the mixture starts to bubble, becomes thicker, and no lumps remain.
Gradually add the vegetable broth, continuing to whisk until fully combined. Bring up to a simmer once again, until bubbling.
Add the salt, black pepper and Boursin cheese. Bring to a gentle boil whisking until the cheese has melted and the sauce is smooth and thickened.
Layer half of the potatoes in the bottom of the prepared baking dish. Pour half of the Boursin cheese sauce evenly over the potatoes. Repeat with the remaining potatoes and sauce.
Top with the shredded mozzarella. Cover the dish tightly with foil and bake for 30 minutes.
Uncover and bake for another 35–40 minutes, or until the potatoes are fully tender when pierced with a knife and the cheese on top is golden brown.
Let rest for at least 15 minutes to allow the sauce to set before serving.
Garnish with fresh chives and enjoy!