Melt the butter with the shallot in a small saucepot over medium heat. Allow to come to a gentle simmer for about 2 to 3 minutes, until the shallot becomes tender and turns light golden brown and the color of the melted butter deepens to a nice golden brown.
Remove the pot from the heat and whisk in the lemon juice, (and the parsley and red pepper flakes, if using). Season to taste with salt and pepper. Drizzle the warm butter sauce over whatever you are serving it with.
Notes
Keep an eye on the butter as it starts to brown. It can go from golden to brown to over-browned very quickly. Remove it from the heat the minute it starts to smell nutty and get to the color you are looking for. The butter will continue to cook and brown slightly even once you’ve removed it from the heat, so err on the lighter side, and you can always return it to the heat for another minute or two.
You can rewarm the lemon butter on the stove. It will start to congeal as it sits. Just 30 seconds over low heat will return the lemon butter to its liquid state, perfect for drizzling.
Whisk or stir the butter and shallots frequently.
Add the lemon juice off the heat. This will keep the fresh flavor of the lemon at its brightest. It is ok, however, to reheat the sauce with the lemon juice and herbs in it if the sauce starts to cool and thicken.