Measure out the milk. Take 2 tablespoons of the milk and combine it with the cornstarch to create a slurry, whisking constantly. Set aside. Add the bourbon to the milk.
Measure out the heavy cream and add the corn syrup to it. Add the mascarpone to a large bowl and whisk in the salt. Set aside.
To make the burnt caramel, I used Jeni’s dry burning technique. You have to keep an eye on the caramel the ENTIRE time! Heat a large (Jeni calls for 4-qt) saucepan over medium heat and add sugar, make sure it is in one layer cover the whole bottom of the pot. Literally watch the sugar until it begins to melt and the outsides turn caramely and melty. Once there is just a small amount of white sugar remaining in the center, use a heat proof spatula and scrape the melted sugar from the sides into the center. Continue to do so until all of the sugar is melted, and stir well. Watch sugar as it begins to bubble and once the edges are bubbly and releasing smoke and the sugar turns a dark amber color, remove from heat. The only way to truly judge it right before it BURN burns is to carefully stand over top and smell/watch. The minute you remove it from the heat, add a few tablespoons of the cream/corn syrup mixture (be careful – it will spit!) and whisk constantly to combine. Slowly add the remaining cream very slowly, whisking constantly.
Place the saucepan back over medium heat and add the milk/bourbon mix. Bring the mixture to a rolling boil (for me, this is over medium heat, and it takes a few minutes to achieve. Do NOT remove your eyes from the milk as it can easily bubble up and over, so have a spatula on hand and turn the heat down if necessary, increasing again slowly) and once boiling, boil for 4 minutes. Remore from heat and whisk in the cornstarch slurry, whisking to combine. Place back over heat and cook for another 1-2 minutes, stirring with a spatula until slightly thickened. Gently pour mixture into the large bowl with the mascarpone and whisk to combine.
Fill a large bowl with ice and ice water, placing an open gallon-sized ziplock bag in the water, bottom down. Pour the mixture carefully into the bag, the press the air out and seal. Chill for 30-45 minutes. Once chilled, set up your ice cream make according to it’s directions and pour the ice cream in. Churn according to directions. For my kitchenaid, I churned for 20 minutes. 5 minutes before finishing, add in toffee pieces. Once churned, spread in a freezer-safe container and place a piece of plastic wrap on top, pressing against the ice cream. Freeze for 4-6 hours before serving. Note: this ice cream is soft!