First, make the Kahlúa hot fudge sauce. Add the chocolate chips, butter, and heavy cream to a small saucepan set over medium-low heat. Cook, stirring occasionally with a silicone spatula, until the mixture is completely melted and smooth. Remove from the heat and stir in the Kahlúa, vanilla extract, and salt. Set aside to cool completely. The sauce can be made up to 2 weeks in advance and stored in an airtight container in the refrigerator until ready to use.

Once the fudge sauce is completely cool, make the ice cream. Line a standard 1-pound loaf pan with parchment paper or set out a large freezer-safe container (if using deli containers, one pint container and one quart container work well for this volume). Set aside.

Add the sweetened condensed milk, espresso powder, Kahlúa, vanilla extract, and salt to a high-powered blender. Blend on medium speed until smooth and fully combined, about 15 seconds.

Add the heavy cream and blend on medium-high speed until the mixture forms soft peaks, about 25 to 30 seconds. Keep a close eye on it and be careful not to overblend, as the cream can split quickly. If your blender isn’t as powerful, this may take a little longer. You’ll know it’s ready when the mixture is smooth, slightly thickened, and resembles softly whipped cream.

Assemble the ice cream. If the hot fudge sauce is too cold to drizzle, microwave it for 10 seconds and stir until it reaches a spoonable consistency. Transfer half of the ice cream mixture to the prepared loaf pan (or fill your containers about halfway if using freezer containers). Top with half of the brownie pieces and half of the hot fudge sauce. Repeat with the remaining ice cream, brownie pieces, and fudge sauce. Use a butter knife to gently swirl everything together a few times to distribute the mix-ins.

Cover tightly with plastic wrap and freeze for at least 8 hours before serving. When tightly covered, the ice cream will keep in the freezer for up to 2 months.