Preheat the oven to 350 degrees . In a medium bowl, combine the flour, baking powder, salt, baking soda and cocoa powder. In a large bowl, beat together the butter and 2 sugars until light and fluffy. Beat in the egg and vanilla. Gradually beat in the flour mixture to form a smooth dough.
Roll out a tablespoon-size ball of dough and place it on an ungreased cookie sheet. Press 4 pretzel sticks firmly into each side of the dough ball. Repeat with the remaining dough and pretzels. Bake until the cookies start to brown around the edges, 7 to 10 minutes.
Place a rack over a sheet of wax paper or foil. Using a spatula, carefully transfer the cookies from the cookie sheet to the racks; let cool completely.
In a double boiler or in the microwave, melt the chocolate chips with the oil; stir to combine. Pour the melted chocolate over each cookie to coat. Cover with chocolate sprinkles. Press 2 red candies into each spider for eyes.