Preheat oven to 350°F. Line two baking sheets with parchment paper.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and sugar on medium-high speed, scraping down the sides of the bowl a couple times, until light and fluffy, about 2 to 3 minutes. Beat in the egg, corn syrup, and vanilla. Scrape down the bowl.
In a medium bowl, whisk together the flour, cocoa, cornstarch, baking soda, and salt. With the mixer on low speed, gradually add the dry ingredients. Beat on low until combined. The dough will be soft and slightly sticky.
Using a 1 ½-tablespoon spring-loaded scoop, drop balls of dough on baking sheets and bake until the cookies are slightly puffed up and the edges are set, about 8 to 9 minutes. Remove baking sheets to cooling racks and remove cookies after a few minutes to continue cooling. Cookies will flatten as they cool.
Decorate the cookies:
For the chocolate drizzle, microwave milk chocolate chips and vegetable oil in a microwave-safe bowl, stirring every 15 seconds until smooth. Drizzle or pipe on top of each cookie. Refrigerate until chocolate is set, at least a half hour.
Make the filling:
Meanwhile, in the bowl of a stand mixer fitted with the paddle attachment, beat the butter on medium speed until smooth. Add the sifted cocoa powder and powdered sugar and beat until light and fluffy, about 3 minutes, scraping down the sides of the bowl as needed. Add in the warm water and vanilla, and beat on medium-high speed for about 2 minutes or until light and fluffy.
Pipe or spread filling on the flat side of half of the cookies. Gently press another cookie on top of the filling.
Serve or store assembled Fudge Rounds in an airtight container at room temperature for up to 1 day, in the fridge for up to 5 days, or freeze for up to 1 month. The colder the Fudge Rounds are when serving, the more fudgy they’ll be!