Prepare the milk and cream mixture. Combine the milk, cream, ½ cup sugar, cinnamon, and a pinch of salt in a medium saucepan. Then, heat over medium heat, stirring occasionally, until the mixture is steaming (approximately 170°F). Remove from heat.
Beat the egg yolks. In a mixing bowl, whisk the egg yolks with the remaining ¼ cup sugar until the mixture is pale and thick. You can use a hand mixer on low speed for efficiency. The color should visibly lighten.
Temper the egg yolks. Gradually add ½ cup of the warm milk to the egg yolks, whisking continuously to prevent curdling. Repeat this process until you’ve incorporated about half the milk mixture. Then, slowly pour the tempered egg yolks back into the saucepan, whisking constantly.
Cook the custard. Place the saucepan over medium heat and stir until the custard thickens and reaches 185°F. You’ll know it’s ready when it coats the back of a spoon, and you can draw a clear line with your finger that stays intact. Do not let the mixture boil. Remove from the heat and stir in the vanilla extract.
Strain and chill the custard. Pour the custard through a fine-mesh sieve or cheesecloth into a large bowl to remove any solids. Then, cover the bowl with plastic wrap, pressing the wrap directly onto the surface of the custard to prevent skin from forming. Chill in the refrigerator for 4-24 hours until thoroughly cold.
Churn the ice cream. Once chilled, pour the custard into your ice cream maker and churn according to the manufacturer’s instructions. The mixture should reach a soft-serve consistency after churning.
Mix in the gingersnaps. Gently fold the crumbled gingersnaps into the churned ice cream by hand to make sure they are distributed evenly.
Swirl in the caramel. Transfer the ice cream to a loaf pan or storage container. Then, drizzle the caramel sauce over the top and use a butter knife to create swirls in a figure-eight motion. Be careful not to overmix; the goal is to create distinct ribbons of caramel.
Freeze until firm. Cover the container with plastic wrap or a lid and freeze for at least 4 hours or until the ice cream is firm.