1. Melt the butter in a 10-inch skillet. Add the pecans and kosher salt. Cook over medium-low heat until pecans are toasted and golden, stirring frequently, about 4 to 6 minutes. Remove from the heat, strain (the butter will have a pecan flavor and can be strained and reserved for another use). Chill the nuts.
2. Combine the milk and cream in a Cuisinart® medium saucepan. Use a sharp knife to split the vanilla bean in half lengthwise. Use the blunt edge to scrape out the "seeds." Stir the seeds and bean pod into the milk/cream mixture. Bring the mixture to a slow boil over medium heat, reduce the heat to low, and simmer for 30 minutes, stirring occasionally.
3. Combine eggs, egg yolks, and sugar in a medium bowl. Use a hand mixer on medium speed to beat until the mixture is thick, smooth, and pale yellow in color (similar to mayonnaise), about 2 minutes. Remove the vanilla bean pod from the milk/cream mixture and discard it. Pour out 1 cup of the hot liquid. With the mixer on low speed, add the cup of hot milk/cream to the egg mixture in a slow, steady stream. When thoroughly combined, pour the egg mixture back into the saucepan and stir to combine. Cook, stirring constantly, over medium low heat until the mixture is thick enough to coat the back of a spoon. Transfer to a bowl, cover with a sheet of plastic wrap placed directly on the custard, and chill completely.
4. Pour the chilled custard into the freezer bowl, turn the machine on and let mix until thickened, about 25 to 30 minutes. The ice cream will have a soft, creamy texture. If a firmer consistency is desired, transfer the ice cream to an airtight container and place in freezer for about 2 hours.
5. Remove from freezer about 15 minutes before serving.