Start the Ice Cream Base: In a saucepan, gently warm 2 cups of heavy cream and 1 cup of full-fat coconut milk over medium heat. Don't let it boil, just heat for about 3-5 minutes until it's steaming slightly.
Prepare Egg Mixture: While the cream heats, whisk together the 3 egg yolks, 1 teaspoon vanilla extract, and ½ cup brown low-carb sweetener in a separate bowl until smooth and light.
Temper the Eggs: Remove the warm cream mixture from the heat and let it cool for just a minute. Slowly pour about half a cup of the warm cream into the egg mixture, whisking vigorously and constantly to prevent the eggs from scrambling. Then, pour the tempered egg mixture back into the saucepan with the rest of the cream.
Thicken the Custard: Return the saucepan to medium heat. Whisk continuously for 5 to 10 minutes until the mixture thickens slightly, enough to coat the back of a spoon. Be careful not to boil it.
Cool the Base: Take the thickened custard off the heat. Stir in the optional 2 tablespoons of vodka. Allow it to cool completely at room temperature, then refrigerate for at least 2 hours (or until thoroughly chilled) for the best creamy texture.
Churn: Once chilled, pour the mixture into the canister of your ice cream maker and churn according to your manufacturer’s directions until it reaches a soft-serve consistency.
Toast the Pecans: While the ice cream base is chilling, preheat your oven to 350°F (180°C). Spread 1 cup of pecans on a baking tray and toast for about 10 minutes, checking halfway through to ensure they don't burn. They should be fragrant and lightly golden.
Coat the Pecans: Transfer the warm toasted pecans to a small bowl. Pour in 2 tablespoons of melted butter, 2 tablespoons of brown low-carb sweetener, and ¼ teaspoon of salt. Mix well until all the pecans are evenly coated in the buttery sweet mixture. Set them aside to cool completely.
Combine & Freeze: Once the ice cream has been churned to a creamy, smooth texture, gently fold in the cooled butter pecan mixture. You can chop the nuts finer if you prefer smaller pieces.
Final Chill: Spoon the ice cream into an airtight container and place it in the freezer for at least an hour, or several hours, for a firmer consistency. To serve, if it’s too hard, let it soften at room temperature for 5-15 minutes for the perfect scoop.