In a large bowl, mix the parsley, capers, gherkins, garlic, smooth mustard and grainy mustard. Whisk to blend, then add the vinegar, lemon juice and olive oil and combine well. Taste for seasoning and add salt and pepper, if needed.
Put the rhubarb on a flat surface. Use a sharp knife to cut the stalks into 3/4 to 1-inch thick "rounds". Heat a large skillet, over medium heat, and add the canola oil. When the oil begins to smoke lightly, lower the heat and add the rhubarb. Stir to coat the pieces with the oil. Season with salt and add the honey. Stir to blend. Cook for another minute, until the pieces soften slightly. Immediately transfer the rhubarb to the bowl with the salsa. Toss to blend and refrigerate until ready to use.
This salsa can be made the day before and left overnight, in the refrigerator, to "rest" so the flavors meld together before serving.