broccoli is a cool weather crop and they say to start it before last frost, around the same time you would start tomatoes. That means starting it indoors in a south-facing window, or even better, a 4 foot fluorescent shop light. I have 3 shop lights just for tomatoes, peppers and other early starts (one of the fixtures is shot and I need a new one). I start anywhere from mid February to very early March indoors and start hardening off after the last expected frost. Hardening off gradually just for a week or so will get them adjusted to the outdoors.