Combine flour, baking soda, salt, and baking powder in a large bowl and stir with a fork to mix ingredients well.
Combine butter, white sugar, and brown sugar in a large bowl; beat with an electric mixer until smooth and creamy. Add eggs and vanilla extract and beat until smooth and fluffy. Add in flour mixture, 1 cup at a time, and mix in with a spatula until well incorporated. Fold in 1 1/2 cups chocolate chips until well combined.
Drop cookies onto ungreased baking sheets. Pour 1/2 cup chocolate chips into a bowl. Push about 3 to 4 chocolate chips onto each cookie, tip-side down, to make the spider bodies.
Bake in the the preheated oven until edges are golden, 10 to 15 minutes. Cool on the baking sheet for 1 minute before removing to a wire rack.
Melt remaining 1/2 cup chocolate in a microwave-safe glass or ceramic bowl in 15-second intervals, stirring after each melting, 1 to 3 minutes. Spoon melted chocolate into a piping bag with a small tip and draw little legs on each side of the spider bodies to create spider legs.