Well I don't know if someone was playing a prank on you and planting eggs in the nest boxes or a neighbour's hens were coming and laying in your nest boxes but I can assure you that more than one egg a day per hen is extremely unusual and not to be expected from any breed. Usually it takes just over 24hrs for an egg to be produced so most birds will lay slightly later in the day each day, until it is too late to lay one that day and they lay it the next morning. So you might get an egg a day for 9-10 days and then miss a day and then an egg a day for the next 10 days or so before another day off. Some high production manage to lay every single day without taking a day off and the record is about 365 for a year but this is extremely unusual and most birds will have a day off here and there in their first year. If you get 340 a year from a young hen you are doing well. Often you get less due to illness, stress, moulting and countless other events. Subsequent years you will get progressively less.
If you want a constant supply of eggs summer and winter then you need to bring young pullets into the flock at regular intervals and not just keep the original hens for several years. You will also find that young hens lay smaller eggs whilst older birds lay bigger ones, so that is something else to consider.
If you want a constant supply of eggs summer and winter then you need to bring young pullets into the flock at regular intervals and not just keep the original hens for several years. You will also find that young hens lay smaller eggs whilst older birds lay bigger ones, so that is something else to consider.