Through the feed opening of a running blender add, 1 at a time, vinegar, thyme, mustard, garlic, honey, salt, and ground black pepper. Leaving the blender running, slowly add the olive oil in a thin stream. Set aside until needed.
Slice the white and tender green parts of the leeks into 1/2-inch diagonals. Heat the olive oil over medium heat in a skillet and saute until tender. Set aside to cool to room temperature.
Slice the corn from the cobs and place in a bowl with the sauteed leeks. Cut the sun-dried tomatoes into 1/2-inch pieces and add to the bowl. Toss with enough of the dressing to coat. Do not feel compelled to use all of the dressing.
Serve garnished with parsley and additional dressing on the side.