Preheat the oven to 350°F and prepare a baking sheet by lining it with parchment paper. Set aside.
In the bowl of a stand mixer, combine softened butter, granulated sugar, and confectioners’ sugar. Mix just until incorporated.
Slowly drizzle in the vegetable oil, followed by the eggs, water, and vanilla extract. Blend until the mixture is smooth and well combined.
In a separate bowl, whisk together the all-purpose flour, cocoa powder, salt, baking soda, and cream of tartar until evenly distributed.
Gradually add the dry ingredients to the butter mixture, allowing the mixer to incorporate them fully. Continue mixing until the dough pulls away from the sides of the bowl, forming a cohesive mass.
Using a cookie or ice cream scoop, portion out the dough into golf-ball-sized rounds and place them on the lined baking sheet. Roll each dough ball between your palms to create a smooth, even shape.
Press the bottom of a clean kitchen glass into granulated sugar, then gently flatten each dough ball, ensuring the center is slightly more compressed than the edges. Repeat for all cookies.
Bake for 7 minutes, then remove the cookies from the oven. They will still be slightly underbaked at this stage, as they will undergo additional broiling.
Carefully press a piece of semi-sweet chocolate onto the center of each cookie, then top with half of a marshmallow.
Place the baking sheet under the broiler for 1 to 1 ½ minutes, keeping a close watch to prevent the marshmallows from browning too much.
Allow the cookies to cool for 5-10 minutes before serving. The chocolate will remain slightly melted, creating a rich, gooey texture with every bite.