Using kitchen shears trim the sharp tips off the leaves. Remove any small leaves at the bottom of the artichoke and trim the stem. In a large lidded pot fitted with a steamer basket, add enough water to reach 2-inches up the pot and bring to a boil over medium-high heat.
Add the artichokes upright to the pot then cover and steam until the bottom leaves pull away easily, about 35 to 40 minutes.
Remove the artichokes from the pot and cut in half lengthwise. Heat a grill or griddle on medium-high heat. Brush the artichokes with the melted butter then place on the grill or griddle cut side down and cook until slightly charred, about 5 minutes.
For the lemon vinaigrette:
In a small pan over low heat, add the olive oil and garlic. Fry the garlic, stirring occasionally until it is crispy and golden brown, about 10 minutes.
Spoon the garlic onto a paper towel lined plate and remove the oil from heat. Let the oil cool slightly then whisk together with the butter, lemon zest, lemon juice and chives.
To serve:
Arrange the artichokes cut side up on a plate, season with salt and pour half of the dressing over the top.
Sprinkle with pecorino and the crispy garlic and serve with the remaining dressing on the side for dipping.