  Topology and electron interactions are two central themes in modern condensed
matter physics. Here we propose graphene based systems where both the band
topology and interaction effects can be simply controlled with electric fields.
We study a number of systems of twisted double layers with small twist angle
where a moir\'e super-lattice is formed. Each layer is chosen to be either AB
stacked bilayer graphene (BG), ABC stacked trilayer graphene (TG), or hexagonal
boron nitride (h-BN). In these systems a vertical applied electric field
enables control of the bandwidth, and interestingly also the Chern number. We
find that the Chern numbers of the bands associated with each of the two
microscopic valleys can be $\pm 0,\pm 1,\pm 2, \pm 3$ depending on the specific
system and vertical electrical field. We show that these graphene moir\'e
super-lattices are promising platforms to realize a number of fascinating
many-body phenomena, including (Fractional) Quantum Anomalous Hall Effects. We
also discuss conceptual similarities and implications for modeling twisted
bilayer graphene systems.
