Preheat oven to 375°F (190°C).
Brown the ground sausage in a skillet over medium heat until cooked through; remove and drain excess fat.
In the same pan, sauté the chopped onion until translucent, then add the garlic and cook for 1 minute.
Sprinkle the flour over the onions to form a light roux and cook for about 1 minute.
Gradually whisk in the chicken broth and cream until smooth, then simmer until the sauce slightly thickens.
Return the browned sausage to the sauce, add thyme, salt and pepper, and stir to combine.
Butter a 9x13-inch (or similar) baking dish and arrange a layer of sliced potatoes evenly across the bottom.
Spoon half the sausage-and-cream mixture over the potatoes; repeat with remaining potatoes and sauce.
Sprinkle shredded cheddar evenly over the top, cover loosely with foil, and bake 35 minutes.
Remove foil and bake an additional 15 minutes until potatoes are tender and cheese is golden; let rest 5–10 minutes before serving and garnish with parsley.