Prepare the Baking Sheet:
Line a cookie sheet with parchment paper and arrange Ritz crackers in a single layer.

Make the Caramel Mixture:
In a small saucepan, combine the sweetened condensed milk, butter, and brown sugar. Cook over medium heat for 7-8 minutes, stirring often to prevent burning.

Add Milk and Vanilla:
Reduce the heat to low and whisk in the milk, vanilla extract, and chopped peanuts until smooth. Continue cooking for an additional 2 minutes, or until the mixture thickens, then remove from heat.

Assemble the Cookies:
Using a cookie scoop or spoon, top each Ritz cracker with the caramel peanut mixture.

Cool and Store:
Allow the cookies to fully cool on the parchment paper. Once cooled, transfer them to an airtight container for storage.