Step 1

Adjust oven rack to upper-middle position and heat oven to 350 degrees. Melt 2 tablespoons butter in medium saucepan over medium-low heat. Add onion and ½ teaspoon salt and cook until translucent, about 5 minutes. Add garlic and thyme and cook until fragrant, about 30 seconds. Add broth, increase heat to medium-high, and bring to boil. Cover and remove from heat.

Step 2

Pulse bread, Parmesan, remaining 2 tablespoons butter, ½ teaspoon salt, and ½ teaspoon pepper in food processor until coarsely ground, 8 to 10 pulses; transfer to bowl and set aside. Combine spinach, cream cheese, ½ teaspoon salt, and ¼ teaspoon pepper in now-empty food processor and process until smooth, about 10 seconds.

Step 3

Spread spinach mixture in even layer in 13 by 9-inch baking dish. Sprinkle rice evenly over spinach mixture. Sprinkle cheddar over rice. Pour broth mixture into baking dish, cover tightly with double layer of aluminum foil, and bake for 25 minutes.

Step 4

Remove casserole from oven, remove foil, and stir to redistribute ingredients. Return casserole to oven, increase oven temperature to 450 degrees, and continue baking, uncovered, until all liquid is absorbed, about 15 minutes. Sprinkle bread-crumb mixture over top and bake until golden brown, 8 to 10 minutes. Let casserole cool for 20 minutes. Serve.