Preheat the oven to 375 degrees F (190 degrees C). Lightly grease baking sheets.

Beat brown sugar, shortening, eggs, and vanilla extract in a large bowl until light and fluffy, 3 to 4 minutes. Sift flour into a separate bowl; whisk in salt and baking soda. Stir flour mixture into brown sugar mixture; stir in peanuts.

Drop dough by rounded teaspoons 2 inches apart onto the prepared baking sheets. Flatten dough with the bottom of a greased glass dipped in sugar.

Bake in the preheated oven until golden brown, 8 to 10 minutes.