1. Wash the potatoes and then cook them in boiling water until they are tender (a knife easily pierces them). Drain and set aside.
2. Wash the Brussels sprouts and then cook them in salted boiling water for 15 minutes. Drain and set aside.
3. Meanwhile, peel the garlic and onion, then slice the onion and chop the garlic.
4. Sauté the garlic and onion in a tablespoon of olive oil until the onion is completely translucent (or starts to caramelize). Set aside.
5. Peel the potatoes, cut them into cubes, then place them in a gratin dish. Cut the Brussels sprouts in half and place them in the same dish. Add the garlic and onion. Season with salt and pepper, then mix with a spoon to evenly distribute the ingredients.
6. In a bowl, mix the cream with whole grain mustard. Pour this mixture over the gratin.
7. Bake for 25-30 minutes at 180°C, until it is gratinated.
8. Enjoy this Brussels sprouts and potato gratin hot.