Preheat the oven to 350 degrees F. Butter a deep casserole dish.
Bring the chicken broth, milk, 1 1/2 teaspoons salt and cayenne to a boil in a medium saucepan. Slowly whisk in the grits and lower the heat to a simmer. Cover and cook, stirring occasionally, until thick, about 30 minutes.
Remove from the heat and stir in the Cheddar and pepper-jack cheeses and butter until melted and smooth; cool slightly. Stir in the eggs and transfer the mixture to the prepared casserole dish. Smooth the top of the grits and then bake until just set and lightly brown, about 1 hour. Let rest for at least 5 minutes. Scatter with the scallions, if using, and cut into squares.
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