In a medium saucepan, melt the butter over medium-low heat. As the butter melts, it’ll start to foam, then turn a clear golden color. Continue to stir the butter, scraping up any browned specks from the bottom of the pan as it starts to brown. It should have a nutty aroma. Once browned and nutty, transfer to a shallow bowl; cool slightly.

In a large bowl, whisk the egg yolks, both sugars, and salt together until mixture is fluffy and lightened in color. Add the brown butter, whisking until fully combined.

Pour the heavy cream and milk into a large saucepan, and stir constantly over medium-high heat until it begins to simmer. Pour about a cup of the warmed cream into the egg yolk mixture, whisking until smooth. Slowly pour the rest of the cream into the bowl, whisking until combined.

Transfer custard back into the saucepan and cook over medium heat until thickened and coats the back of a spoon, about 5-8 minutes.

Immediately pour the custard mixture through a fine mesh sieve over a bowl or large glass measuring cup. Whisk in the vanilla until smooth. Cover and chill the mixture thoroughly in the refrigerator, about 4 hours.*

Once the custard is chilled, freeze in an ice cream maker, following the manufacturer's instructions. While ice cream is churning, place the dulce de leche in a microwave-safe bowl and warm in the microwave about 15-20 seconds, or until less thick and a softer consistency.

After ice cream is done churning, gently fold in the toffee bits by hand with a silicone spatula. Pour a third of the ice cream into a freezer-safe container, then dollop a third of the warmed dulce de leche over top. Layer another third of the ice cream on top, followed by another third of the dulce de leche. Repeat with remaining ice cream and dulce de leche. Using a knife or skewer, swirl figure-eights throughout the ice cream. Cover and freeze for at least 4 hours, and up to 3 weeks. Scoop and enjoy!