Combine olive oil, lemon juice, garlic, rosemary and salt and set aside

Artichokes will brown where cut quickly, so don't start preparing them ahead of time. 

Fill a bowl with water just enough to cover the artichokes and squeeze the other half of the lemon into the water

Trim the leaves just to cut the points off (optional)

Cut of the very tip of the whole artichoke

Cut the artichoke in half and scoop out the bristles in the middle with a soup spoon.

Immediately drop the artichoke half in the lemon water before you start on the next half.

Prepare a pot with a steamer rack over boiling water.

Place your artichoke halves on the steamer rack, reduce heat to medium, cover pot and let steam for 20 minutes

Prepare your grill. 

Set aside 2 teaspoons of marinade

After 20 minutes, remove the artichoke halves and brush the olive oil marinade over the halves...tucking the sauce between the leaves.

Place the artichoke halves, cut side down on the grill and cook for 10-15 minutes.

Remove from the grill and serve with butter dipping sauce. 

To enjoy the artichokes, pull the leaves off and use your teeth to draw the meat (closest to the stem) off of the leaf. Eat as is or dip it in your favorite sauce. Once you've enjoyed all leaves, the nugget of meat in the middle...the heart...is pure goodness. Close your eyes and savor.

Place butter in microwave-safe container and melt until almost liquid. Add in the reserved 2 teaspoons of herb oil and microwave on medium for another 20-30 seconds. Microwave strengths vary, you don't want it to sizzle and pop...just a slow warming until the flavors meld.

Re-warm as necessary before serving