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Preheat the oven to 375°F.
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Grease a 9”x13” rectangle or oval casserole dish with cooking spray and set aside.
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In a large pot, add the oil, onion and broccoli. Turn the heat to medium and saute for 5 minutes. Mix in the garlic and thyme and cook for 2 more minutes.
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Add the rice and 4 cups of water. Mix together. Turn the heat to high and bring to a boil. Immediately reduce the heat to low, cover and simmer for 12 minutes until partially cooked through.
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Mix in the milk, broth and salt and bring to a boil. Simmer on low, uncovered, for 5 minutes until mostly thickened.
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Mix in 1 1⁄2 cup of the shredded cheese. Be sure to taste and adjust salt to your liking.
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Transfer the cheesy rice mixture to the prepared pan and spread into an even layer.
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Sprinkle with remaining 1 cup shredded cheese.
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Bake uncovered for 25 minutes until bubbly and golden.
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Remove from the oven and let cool for 8-10 minutes before digging in!