In a small bowl, stir together flour, baking soda, and baking powder. Set aside.
In a large bowl, cream together the butter and sugar until smooth. Beat in egg and vanilla. Gradually blend in the dry ingredients until dough is formed. Add oreos directly into batter and beat on low speed until oreos are crushed into small pieces and blended into dough.
Using a 1.5 tbsp cookie dough scoop, scoop out dough and place into 16 shot glass molds. Using a very small spatula or spoon, spread the dough completely across the bottom of each shot glass mold. Make sure you don't leave any gaps, otherwise, your cookie glass will have holes. I recommend smashing the dough down to really compact it and to the point that the sides of the silicone mold are bulging, and then slowly pushing some of the dough back up so that the silicone mold goes back to its form.The silicone molds should be transparent enough for you to examine for any gaps. Your dough should cover about half of the cookie shot glass mold. Add a second 1.5 tbsp scoop of dough to the molds. Again, spread it across evenly on the sides and also on the top. You should have a thin layer that fully covers the surface. Add about another 1/2 tbsp of dough to cover any remaining gaps and to level the surface. Your dough surface should be just a hair shy of reaching the top edge of the mold (see photo above). You also want to make sure the sides of the shot glass molds are even. Some of the shot glasses may have lost their form in your effort to smash the dough in and you want to make sure all the walls/sides are even again before you bake (see photo above).
Preheat oven to 350°F. Place your silicone molds onto a baking sheet. Place another baking sheet on top of the molds. This will help prevent the cookie shots from rising too much out of the molds while baking.
Bake for approximately 24 minutes once your oven is heated to 350°F. You want to make sure the cookies are completely done, otherwise dough will be too soft. Allow the cookies to cool.
Once cooled, use a sharp serrated knife and cut off any cookie dough that may have risen past the molds, so that your cookie glasses will have a flat, even bottom. Place cookies, still in molds, into your freezer for several hours, until cookies are frozen solid.
Once frozen solid, cookie shots should come off the molds pretty easily and in one piece. You may find that despite your best efforts, a few cookie shots may have a small gap/hole. As long as it is small, these are still useable. They won't be as pretty, but once you coat them with chocolate, it should seal the small gaps.
Melt your chocolate on the stovetop. Bring a small pot with water to a simmer. Place a large glass mixing bowl on top of the pot (make sure your bowl is big enough that it won't touch the water or the botto of the pot) and add in the chocolate and oil. Stir until chocolate is completely melted and smooth. You want the chocolate consistency to be thin enough to easily spread inside the molds, but also thick enough to provide a seal foor your cookies.
Once chocolate is completely melted, turn off stove, but keep bowl over the pot. Working quickly, use a small spatula to spread white chocolate evenly across the inside of each shot glass, making sure every to coat the entire interior, so that any liquid you pour in does not leak through.
Place shot glasses back in freezer for a few minutes, until chocolate solidifies. I recommend keeping shot glasses in the freezer until shortly before serving. They will defrost and come to room temperature in about 10-15 minutes. Add your milk or other liquids, right before serving. If you properly coated them, they are able to hold liquids for a little while. Time will vary depending on the temperature of the room. I found that after 30 minutes in my warm house, the cookies and chocolate start to soften and some of them had milk starting to come through.