Preheat oven to 375°F (190°C) and grease a 9x13 inch baking dish.
In a large skillet over medium-high heat, cook and crumble the sausage until browned. Remove sausage and set aside, reserving 1 tablespoon of fat.
Add diced onion to the skillet and sauté for 4-5 minutes until translucent. Add garlic and cook for 1 additional minute.
In a large bowl, whisk together the heavy cream, chicken broth, thyme, salt, and pepper.
Layer half of the sliced potatoes in the bottom of the prepared baking dish. Top with the cooked sausage, onions, asparagus, and peas.
Arrange the remaining potatoes on top and pour the cream mixture evenly over the casserole.
Cover with foil and bake for 40 minutes.
Remove foil, sprinkle with shredded Gruyère cheese, and bake for an additional 10-15 minutes until potatoes are tender and cheese is golden brown.
Let stand for 10 minutes before serving.