Preheat oven to 400°F (200°C).

Butter a 13 x 9 x 2 inch glass baking dish.

Overlap one-third of the potato slices in the prepared dish.

Season with salt and pepper.

Sprinkle with 1/2 teaspoon of dried dillweed and 1 cup of grated Gruyere cheese.

Repeat the layering process twice, using one-third of the remaining potatoes, 1/2 teaspoon of dried dillweed, and 1 cup of grated Gruyere cheese for each layer.

In a bowl, whisk together the whipping cream, chicken broth, and Dijon mustard.

Pour the cream mixture evenly over the layered potatoes.

Bake in the preheated oven for approximately 1 hour, or until the potatoes are tender and the top is golden brown and bubbly.

Let the gratin cool for 10 minutes before serving.