• Before proceeding, be sure you have a prebaked pie crust ready in a 9" or 10" pie plate.

For the Butterscotch Filling

• Whisk together milk, half and half, and egg yolks until fully combined. Save the egg whites for the meringue portion of the recipe.
• Add butter and brown sugar to a medium saucepan over medium-low heat, whisking occasionally until large bubbles begin to form and the brown sugar smells nutty--about 5 minutes.
• Whisk flour and corn starch into the buttery brown sugar mixture until dissolved, about 30 seconds.
• Slowly stream in the milk and egg mixture over a period of 1 minute, constantly whisking until fully combined. Be careful, as the mixture may sputter at first.
• Continue to cook the butterscotch filling, continuously whisking until the mixture begins to bubble and reaches roughly 180°F / 82°C--about 3 to 5 minutes. Remove from the heat and stir in the vanilla until combined.
• Using a mesh strainer held over the prepared pie crust, pour the butterscotch filling through, leaving about ½"-¼" space from the top of the crust. Set aside the pie to allow the butterscotch filling to cool as you move onto the meringue.

For the meringue topping

• Add egg whites to a stand or hand mixer bowl, and set aside.
• In a small saucepan, whisk together sugar and water over high heat until the sugar is dissolved. If using cornstarch, mix it with 2 TBSP of cold water in a separate bowl until a slurry forms. Slowly whisk the slurry into the hot sugar mixture. Once incorporated, stop whisking but continue cooking over high heat.
• Continue cooking the mixture over high heat until it starts to bubble around the outer edges, then lower the heat to medium. About 5-7 minutes. Keep an eye out, especially around this period, as the mixture may try to overflow when it begins to boil. If that occurs, remove the saucepan from the heat for a moment and then resume cooking.
• Use a digital or candy thermometer to check the temperature of the mixture. Once it reaches 230°F / 110°C in the center of the liquid, about 3-4 minutes longer, start whipping the egg whites over low speed until frothy.
• Add cream of tartar to the egg whites, and increase the speed to medium until medium-soft peaks form. Once the sugar syrup reaches 240°F / 115°C, remove it from the heat.
• Whip the egg whites over low speed as you slowly stream the hot sugar liquid down one side of the bowl over a 1 minute period, aiming for the edge of the whites but avoiding the whisk so that the hot liquid doesn't splatter.
• Add the vanilla, and begin whipping the egg whites over medium-high speed until stiff peaks form and the meringue is shiny.

Finishing the Pie

• Add as much meringue topping as desired to the top of the pie, being sure to cover the surface of the butterscotch filling up to the edge of the crust.
• Place the pie under the oven broiler for 5-8 minutes, occasionally turning to be sure the top browns evenly but doesn't burn.
• Let the pie cool to room temperature, then place it uncovered in the refrigerator to cool for 2-3 hours. Once served, stick toothpicks into the top of the meringue and lightly cover the pie in plastic wrap, storing in the refrigerator for up to 3 days.