Spicy Potato Gratin

Name: Spicy Potato Gratin
Ingredients: 2 tablespoons unsalted butter, at room temperature; 3 cloves garlic, minced (about 1 tablespoon); 1 shallot, finely diced; 1 teaspoon all-purpose flour; 1 cup milk; 1 cup heavy cream; 3 tablespoons chili crisp; 1/2 cup grated Gruyère cheese; 1 tablespoon chopped thyme leaves; 1 1/2 teaspoons kosher salt; 1 teaspoon freshly ground black pepper; 3 pounds russet potatoes, rinsed and scrubbed clean; 1/4 cup grated Parmesan cheese; 1 green onion, chopped, for garnish