I always prefer to have both ends of the mooring line tied to the boat, if possible. Just loop the line through the cleat, ring, bollard or whatever. OXOs are best, if you have sufficient room on your boat's cleat. I often use the method preferred in the USA of tying to a cleat rather than the RYA preferred OXO as I can easily tie two lines to the one cleat.
Where long lines ashore are needed, as is common practice in Turkey and Greece, I generally loop the shore end around a smooth object and tie a rolling hitch back along the mooring line so that I don't need to go ashore to untie but merely use the dinghy to untie the knot over the water near the shore. This knot is easy to tie and untie under tension. This way, I don't need to let out the anchor to untie the knot and the boat will spring away from the shore as the knot is untied.
There is nothing inherently wrong with a round turn and two half hitches but I have found that wrapping twice through a ring is a bit painful, particularly if excess line is thrown ashore.
In the rare cases where I have had to have a crew member step ashore to stern tie to a ring, I pre-tie the Bowline using the "overhand knot with a loop" method so that the bowline can be tied by merely looping the end of the line through the ring, pass it through the loop and collapse into a bowline. This method takes a fraction of a second to tie as the knot is almost completely tied on the boat beforehand. It needs a bit of practice but it is worth it.
Craig
s/v "Shirley Valentine"
Gold Coast, Australia