Preheat the grill to a medium heat. Once you're ready to grill turn it down slightly to a medium-low heat.
Place the butter in a cast iron skillet with the shallots. Place on the bottom grill rack. Allow to cook for about 8 to 12 minutes, depending on your grill. Keep an eye on it. You want the butter to start to brown beautifully, without starting to burn. Keep moving the shallots around in it, they will start to crisp up as the butter browns. The taste is amazing. Warning you now.
Snap the asparagus so you get rid of the woody ends. Rinse, and dry them. Place them on the grill, allow them to cook for about 4 to 6 minutes on each side. Flip over when they start to char a little on the ends.
Once the butter is almost amber, and the asparagus is just starting to char a bit, take tongs and toss the asparagus in the cast iron pan with the butter. Move them around until the asparagus is coated with butter and shallots.
Carefully (that pan is freaking hot, so use gloves!) remove the pan from the grill and transfer the asparagus to a serving dish.
You can hit the asparagus with lemon and/or salt if you like. Totally optional. A splash of olive oil is nice too. Adds a bit more flavour.
Serve with a big old addicted to asparagus in brown butter smile!