Melt butter in a medium sized, heavy-bottomed, saucepan set over medium-low heat. Add brown sugar and cayenne pepper (if using). While stirring gently and very slowly, bring the mixture to a boil slowly and over steady heat. Use a candy thermometer to check the temperature. Continue stirring very slowly and gently (it is a slow process). Boil 3-4 minutes or until the thermometer registers 270°-290°F and becomes lighter in color and “fluffier”. Turn off the heat and add the oyster crackers."
Now, working quickly so the brown sugar/butter mixture doesn’t set up, pour the toffee/oyster crackers onto the prepared baking sheet and try to spread them out to a single layer. (If it is too difficult to spread the crackers into a single layer at this point, don’t worry – it will be possible in a few minutes.)
Sprinkle the crackers lightly with coarse sea salt or kosher salt.
After a total 5 minutes baking time, remove from oven and place the pan on a cooling rack to cool for 5 minutes.