Make the Butter Brickle Toffee: Melt butter in a saucepan over medium heat. Stir in brown sugar and salt, cooking until the mixture thickens and turns golden (about 5–7 minutes). Remove from heat, add vanilla if using, pour onto a parchment-lined baking sheet, spread thin, and let cool completely. Break into small pieces.
Prepare the Ice Cream Base: Whisk together heavy cream, milk, sugar, vanilla, and salt until sugar dissolves. Chill in the refrigerator for 1–2 hours.
Churn the Ice Cream: Pour the chilled base into an ice cream maker and churn per manufacturer instructions (about 20–25 minutes) until it reaches soft-serve consistency.
Add Toffee and Freeze: Add the butter brickle pieces during the last 5 minutes of churning to mix evenly. Transfer ice cream to a container and freeze at least 4 hours until firm.