Slice the tops off the artichokes, pull off the small leaves, trim the stems and snip off the thorny tips. In a large pot, bring 2 inches of water to a boil. Add 1 tablespoon kosher salt, the juice of 1 lemon and the artichokes. Cover and steam until the artichoke bottoms pierce easily, 20 to 40 minutes, depending on size. Drain the artichokes.
When cool enough to handle, cut each artichoke in half lengthwise. Scrape out and discard the fuzzy center.
Preheat a grill to medium direct heat.
Brush the artichokes with the oil, season with salt and pepper and grill, cut-side down, until lightly charred, 6 to 8 minutes. Flip and grill briefly to heat through.
Arrange the artichokes on a platter, drizzle with some of the Green Goddess Dressing and garnish with lemon wedges.
Green Goddess Dressing:
Combine the mayonnaise, creme fraiche, parsley, chervil, tarragon, chives, garlic, anchovy fillets and lemon juice in a food processor and process until smooth. Season with salt and pepper. Add a teaspoon of honey, or to taste. With the machine running, drizzle in just enough oil to thicken slightly. Cover and refrigerate for at least 30 minutes before serving to allow the flavors to meld.