Second block

A 1x2x3 block on the right, without breaking the first.
Each block is a 1x2x3: the left (or right) centre, the two edges and two corners around it on the bottom half, and the bottom edge between. The first block is built anywhere on the cube; the second is built on the other side using only R, r, U and M so the first stays put.
First block (left): R, r, U and M leave it alone.
R U R' U2 M' U R2 r U' M
Both blocks: only the top corners, the top edges and the M slice remain.
M U M' U2 M U' M' U
  • •
    Start with the bottom edge (DL) and the centre, then add a 1x2x1 square and extend it.
  • •
    Use M and r freely: the M slice is solved last, so moving it costs nothing.
  • •
    Pair a corner with its edge in the U layer, then insert the pair with R or r moves, much like an F2L pair.