In a food processor, add the Oreo cookies and pules until medium crumbs.
In a large bowl with electric beaters, or using a stand mixer, whip together mascarpone cheese, powdered sugar, and coffee liqueur until fluffy. Add heavy cream and whip until stiff peaks form; about 4-5 minutes.
Divide mixture in half, leaving 1/2 in mixing bowl and adding other to separate bowl ready for use.
With 1/2 of the mixture still in the mixing bowl, add the cocoa powder and espresso and mix until fully incorporated.
Layer the mixture - chocolate, white, Oreo - into glasses using spoon or by adding mixture to piping bags and piping into glass.
Serve immediately or refrigerate until ready for use, no longer than 2-3 days covered.