In a bowl, whisk together the flour, baking powder, sugar, and half of the salt.
Cut 6 tablespoons of the cold butter into small pieces and mix into the dry ingredients until the mixture looks crumbly. Add the vegetable oil and stir to combine.
Gradually add the water and stir until a wet dough forms. It will be slightly sticky but should stay together. If it's still too crumbly, add a small amount of water little by little until the dough comes together.
Wrap the dough tightly in plastic wrap and refrigerate for 1 hour to help it come together and make rolling easier.
On a floured surface, roll the dough out to about 1/8-inch thickness. Use a round cutter with ridged edges (about 1 1/2inches) to cut out circles.
Preheat your oven to 400°F. Place the dough rounds on a parchment-lined baking sheet.
Use a toothpick to poke a few holes in each cracker to prevent puffing. Brush with the beaten egg and sprinkle with the remaining salt.
Bake for about 9-12 minutes until the crackers are golden. Melt the remaining butter and brush it onto the crackers while they are still warm for extra flavor.