I didn’t make it to Dickie Brennan’s Bourbon House (144 Bourbon St., New Orleans, La.; 504-522-0111; bourbonhouse.com) for a Reveillon dinner.

But there was always lunch. I didn’t want to leave New Orleans without enjoying a plate of shrimp and grits. One of New Orleans top seafood restaurants seemed like just the right place.

With plump shrimp, spicy sausage, and creamy grits, the dish (at right) hit all the right flavor notes. I’d always assumed that the restaurant took its name from its location on the French Quarter’s fabled Bourbon Street. But it turns out that proprietor Dickie Brennan, scion of a celebrated family of New Orleans restaurateurs, is a Bourbon connoisseur. The bar stocks about 250 American whiskeys. It’s said to be the most extensive Bourbon list in the city.

It was too early in the day for an Old Fashioned, but Brennan did persuade me to try a frozen Bourbon milk punch. The creamy drink went down smoothly. “It’s all about slow living,” Brennan said. “It’s the way the holidays should be.”

Bourbon House generously shared the recipe. Its simplicity exemplifies Brennan’s observation about slow living. To channel New Orleans’ festive spirit, I’m thinking of serving it on New Year’s Eve.

Bourbon House’s Frozen Milk Punch

Makes 6 servings

• 4 cups vanilla ice cream
• 1 cup bourbon
• 1/2 teaspoon vanilla extract
• 1 teaspoon simple syrup
• Freshly grated nutmeg

Combine all ingredients except nutmeg in a blender and blend 8 seconds, until slushy. Garnish with nutmeg and serve.