Combine the butter, Worcestershire, oil, garlic and Cajun seasoning in an 8 x 8 x 2-inch casserole dish.
Place dish in the oven just until the butter melts, about 5-10 minutes.
Add shrimp and toss to coat shrimp with the butter mixture.
Return dish to the oven and bake just until shrimp turn pink and opaque, about 10 minutes.
For the grits:
In a medium saucepan, bring the chicken broth to a boil over medium high heat.
Add the grits and heavy cream or whole milk. Return to a boil.
Cover the pan and reduce the heat to low. Simmer until the grits are creamy and most of the liquid is absorbed - about 12 minutes. Stir every few minutes to keep the grits lump free.
Remove the grits from the heat and add two tablespoons of butter. Stir until the butter is melted.
Season with salt and pepper to taste.
Ladle grits into a bowl. Arrange several of the shrimp over top.