In a small saucepan, combine the finely chopped shallots, white wine, and half of the lemon juice.
Bring to a simmer over medium heat and cook until the liquid has almost completely evaporated.
Reduce the heat to the lowest possible setting.
Add a few pieces of the cold butter to the saucepan and whisk constantly until they are almost fully melted.
Continue adding the remaining butter, a few pieces at a time, whisking constantly to create a smooth, emulsified sauce. It is crucial not to let the sauce boil, or it will separate.
Remove the sauce from the heat.
Season to taste with salt, white pepper, and the remaining lemon juice.
Keep the sauce in a warm place until ready to serve.
Bring a large pot of salted water to a rapid boil.
Add the broccoli florets and cook for 3-4 minutes, or until tender-crisp.
Immediately drain the broccoli well.
Transfer to a serving dish and pour the warm lemon butter sauce over the top to serve.
Add a pinch of red pepper flakes with the shallots for a little heat, or stir in some finely chopped fresh parsley or chives at the end for extra freshness.