Brown the butter. In a small saucepan, melt the butter over medium-low heat. Cook the butter, stirring and scraping the bottom occasionally, until it begins to bubble and pop. Continue cooking until it starts foaming and you can see dark brown flecks swimming in the butter when you stir. You’ll know it’s done browning when you no longer hear bubbling and popping — as that’s when all the water has been cooked off. Transfer to a medium mixing bowl and place in the fridge until it is just barely warm.
In a food processor, blitz a half cup of the rolled oats until very finely ground. Add in the flour, cornstarch, baking soda, baking powder, salt and cinnamon and pulse a few times to mix. Set aside.
Once the browned butter has cooled down, whisk in the molasses, dark brown sugar and vanilla extract just until combined and glossy. Whisk in the egg.
Dump in the dry ingredients and fold them into the wet ingredients. Once the mixture is almost totally combined, add in the oats and keep folding until the last streaks of flour disappear.
Scoop out about 20, 1-ounce dough balls (I used a heaping #40 scoop) and chill them in the refrigerator, covered, for at least 1 hour, or until completely firm.
Place 8 cookies on a half sheet tray and bake
Preheat the oven to 350°F. Bake for 6 minutes, then tap the tray against the rack to deflate the cookies and help them spread. Rotate the tray and continue baking for 3 to 4 more minutes or until the cookies are browning around the edges, and the center is just barely set. Transfer to a wire rack and repeat with remaining dough balls.
While the cookies are cooling, make the cream cheese filling. Using a hand mixer, or in the bowl of a stand mixer with a paddle attachment, beat the cream cheese and butter until combined. Add in the powdered sugar, heavy cream, salt and vanilla extract and continue to beat until fluffy and smooth, about 1 minute.
Using a piping bag fit with a round tip, or using a zipper bag with the corner cut off, pipe a swirl of filling onto 10 of the cookies. Leave enough room around the edges for the filling to spread when they are sandwiched with the tops. Then, top each with the remaining 10 cookies, pressing down just so that the filling comes to the edges.