In a food processor, combine all the crust ingredients and blend into a homogeneous mixture. If needed, blend in 1 tablespoon of water at a time until the mixture is slightly sticky, like wet sand.
Transfer the crust mixture into a cake pan (I used an 7-inch springform pan), and press into a flat, even crust. Set aside while you prepare the ice cream filling.
Make the filling: combine bananas, lemon juice, and coconut milk in the food processor and blend until smooth.
Pour approximately 2/3 of the mixture into the cake pan, on top of the prepared crust. Smooth out the top with a spatula.
Mix matcha powder into the remaining ice cream mixture, then pour it over the plain layer. Lightly wiggle the pan to flatten the filling. (If the ice cream mixture is quite solid at this point, you may have to smooth out the top with a spatula.)
Place the cake into the freezer to set for 3+ hours. To serve: let thaw for 10 minutes before slicing with a hot knife.