In a medium saucepan, heat the creams until steaming. Meanwhile, in a medium bowl, whisk together the egg yolks, brown sugar and salt. Pour some of the hot cream into the egg yolk mixture, whisking constantly. Return the mixture to the pot, whisking constantly until it bubbles and thickens. Remove from the heat and stir in the bourbon. Scrape into a bowl, cover and refrigerate until well chilled.
Heat the blueberries, sugar and a squeeze of lemon juice in a medium skillet set over medium-high heat and cook, stirring, until the berries soften and burst, releasing their juices. When the fruit is soft and jammy, remove it from the heat, scrape it into a bowl and refrigerate until well chilled.
Freeze the custard in an ice cream machine according to the manufacturer's directions. When the ice cream is frozen but still soft, scrape the berries in through the feed tube and continue until the mixture is well blended and resembles ice cream. It will still be soft; if you like, scrape it into a loaf pan or other container and freeze until firm. Makes about 3 cups.