I go straight to the experts.
If you've never grown broccoli before (and this is our first time, too) and you're a fly-by-the-seat-of-your-overalls sort of gardener in an unseasonally warm spring, you might get in trouble. You might start to see tiny buds that resemble broccoli forming on your plants. You might get excited, but acknowledge their tiny size and carry on your business. The next day, your tiny buds might be flowers and you might scratch your head wondering how you missed part where the broccoli plant grew broccoli. You might realize too late that your plants are not supposed to flower.
When you turn to gardening books for advice, they will make you feel like an idiot by giving you advice about preventing the flowers. They will cause you to fear that it's too late.
But don't despair! Luckily for all of us, your beautiful broccoli flowers are as edible as the rest of the plant, and they taste kind of like broccoli and kind of like honey. If the buds are still semi-closed, the flowers should hold their shape if they're cooked, but they're lovely in a salad or as a greenhouse snack. While you're eating the flowers, go ahead and eat the leaves and stalks, too. Put aside your fear that they'll be woody and tough like the stems of the store-bought vegetable: unless you grow your broccoli til the stalks are the size of small tree trunks, the whole plant will be delicious.