Wash the artichokes. Cut off the top inch and the stems of the artichokes. Trim the tips of the leaves with kitchen scissors.
Place a steamer basket in a large pot of water. Add the artichokes. Bring to a boil and reduce heat to simmer. Cook for 35 to 40 minutes or until the leaves come out easily when pulled. Alternatively, you can use an electric pressure cooker for 20 to 25 minutes.
While the artichokes steam, make the vinaigrette. Chop the cilantro and put in a medium bowl. Add the red wine vinegar, lime juice, mustard, and honey and season with salt and pepper.
Whisk to combine. Slowly pour in the olive oil, whisking continuously, until it thickens slightly and comes together.