Lars Petrus Method
2. The 2x2x3
block
We expand our existing block with another 1x2x2 block, without destroying the 2x2x2 block if it’s possible. For this reason we mostly turn only R, F and U. We can break the block if we can do a good shortcut, but it’s possible to build the new block without that.
The way is similar to the previous ones: make a corner-edge pair, bring an another edge to its color, finish the 1x2x2 and add this to the 2x2x2 block. Our opportunities are a bit limited, but it’s not a big problem.
See this example:

If we try R’, we can see, that the edge will wrongly connect to the corner. So we have to connect them on the other side: U2R2. If we choose the other edge: With F’D’ we get a corner-edge pair, but we also destroy the first block... We should connect them somewhere else: F’RF’ or F’R2U’. By the second one it would be long to bring the BlueRed edge to its color, F’RF’ is better. But let’s say we choose U2R2.

We bring the other edge to its color(to the blue): F2. If we look ahead: We will have to turn the F side again because of the corner-edge pair anyway, so rather FR’F.

Put these to parts together: R2. Add this 1x2x2 block to the others(no more then one turn): U2.

Or see another example, where we destroy the previous parts for a little time, so we need less turns(and solving time).

According to the technique above f.e. here’s a solve: URU2R’F2U2RF’U2FU. Well, that is long. This is much faster: BU2B’ adds one edge, L’UL the other one. Finished.

We can look ahead here, too: bring the other edge to its color while building the corner-edge pair, etc.
There are very good examples for block building on Lars Petrus’ site:
http://www.lar5.com/cube/blox.html
Back to the Lars Petrus method
Back to the 2x2x2 block
Go to the edge orientation