Cook shallot:
Melt 1 tablespoon of the butter in a large saucepan over medium-high. Add shallot, and cook, stirring occasionally, until softened and translucent, about 2 minutes.
Cook Grits:
Add broth, milk, salt, and pepper to saucepan, and bring to a boil over medium-high. Slowly whisk in grits, and reduce heat to medium. Cook, whisking often, until grits are thickened and tender, about 5 minutes.
Add cheese to Grits:
Remove saucepan from heat; whisk in cheese, cream, and remaining 1 tablespoon butter until smooth. Cover and keep warm.
Cook shrimp:
Heat oil in a large nonstick skillet over high. Add shrimp, and sprinkle with salt; cook, undisturbed, until golden brown, about 2 minutes. Flip shrimp, and cook, undisturbed, until lightly browned but not cooked through, about 1 minute. Transfer to a plate.
Cook sausage:
Reduce heat in skillet to medium-high; add sausage, and cook, stirring occasionally, until browned, about 4 minutes.
Stir in onion, bell pepper, and celery; cook, stirring often, until tender and beginning to brown, about 3 minutes.
Add seasoning:
Add tomato, garlic, Cajun seasoning, and black pepper to skillet; cook, stirring constantly, until fragrant, about 1 minute.
Finish New Orleans Shrimp:
Stir broth, cream, lemon juice, and Worcestershire into skillet; cook, stirring occasionally and scraping up browned bits from bottom of skillet, until slightly reduced and thickened, about 10 minutes. Return shrimp to skillet, and coat in sauce; cook until cooked through, about 1 minute.
Garnish and serve:
Serve shrimp over grits; sprinkle with scallions.