Preheat your oven to 425 degrees Fahrenheit.
In a medium saucepan, melt the butter and brown sugar over medium heat. Stir occasionally, and bring the mixture to a gentle boil. Allow it to boil for about 5 to 6 minutes.
Prepare a rimmed baking sheet by lining it with parchment paper, a silicone mat, or greased aluminum foil.
Lay the saltine crackers on the prepared baking sheet. They can be slightly overlapped, but try to cover the entire surface of the sheet.
Once the butter and brown sugar mix is ready, carefully pour it over the crackers.
Place the baking sheet in the preheated oven and bake for about 4 to 5 minutes.
After baking, remove the sheet from the oven. Immediately pour the white chocolate chips over the hot mixture. Let them sit for about 5 minutes to soften.
Using the back of a wooden spoon or a spatula, gently spread the melted white chocolate over the crackers.
Sprinkle a pinch of Kosher salt evenly over the surface of the melted chocolate.
Allow the toffee to cool on the counter for a few minutes before sprinkling the crushed peppermints on top.
Next, place the entire baking sheet into the fridge or freezer until the chocolate hardens.
Once set, remove the toffee from the baking sheet. Break it into pieces or cut it with a knife or pizza cutter.
Store the pieces in a resealable container.