Mix flour, butter, sugar, and vanilla extract in a bowl until dough is smooth. Reserve 1/4 the chocolate chips; stir remaining chips into dough until evenly distributed. Roll dough into 24 small logs and place a baking sheet.
Bake in preheated oven until slightly golden around the edges, 15 to 20 minutes. Cool in baking sheet for 10 minutes before removing to cool completely on a wire rack.
Melt shortening in a small saucepan over medium-low heat; stir in remaining 1/2 cup chocolate chips until melted, about 5 minutes. Dip cookies into chocolate and return to baking sheet. Refrigerate until firm.