Preheat oven to 425°F. Butter a 2-quart baking dish and set aside.
Bring a large pot of salted water to a boil. Add broccoli rabe and cook until just tender, about 2 minutes. Transfer to a bowl of ice water to shock. Drain, gently squeeze out extra liquid and set aside.
Place breadcrumbs, 1/2 cup parmesan, thyme, and a pinch of salt and pepper in a small bowl.
Melt butter in a large pot. Scoop out 2 tablespoons and drizzle it over breadcrumbs. Toss to combine; set aside. Add garlic to pot and cook until fragrant, about a minute. Whisk in flour and cook, stirring, for 1 minute. Add the milk, cream and 1 teaspoon salt; bring to a boil while whisking constantly. Lower the heat and simmer, stirring occasionally, until sauce is thickened, about 5 minutes. Whisk in remaining 1 cup parmesan until melted; season with salt and pepper. Stir in broccoli rabe and transfer to prepared dish. Sprinkle with breadcrumb mixture.
Bake for about 20 minutes, until the sauce is bubbling and the crumbs are browned on top. Let stand for 15 minutes before serving.