Heat oven to 350. Coat a 13 x 9 baking dish with butter.
Melt butter in a large frying pan over medium heat. When it foams, add scallions, onion, garlic, 1/2 tsp salt and pepper. Cook, stirring occasionally, until vegetables are tender but not browned, about 7 minutes.
Add rice and stir to coat in butter. Add broth, cream, and remaining 2 tsp salt. Bring to a simmer, stirring frequently. Remove from heat, stir in 1 cup of cheese, pour into the prepared dish, and spread evenly. Cover with aluminum foil and bake until most of the liquid has been absorbed and the rice is almost cooked, about 30 minutes.
Uncover, evenly sprinkle remaining 1/2 cup cheese over top, and continue baking until rice is tender and cheese is golden, about 15 to 20 minutes more.