Place the potatoes into a large pot, and then cover with water by 2 inches. Swirl in salt as it suits you, and then bring it all to a boil over medium-high heat. Turn the heat to medium and simmer until the potatoes yield easily when pierced with a fork (5 - 10 minutes), but aren't completely tender.
Drain the potatoes in a colander, and then let them cool to room temperature.
Preheat the grill to 350 F, and then cut the potatoes cross-wise into ⅛-inch thick slices. Brush them with olive oil, and then grill about 8 minutes per side.
Making the vinaigrette
Toss the chopped shallot into the bottom of a large mixing bowl and then add the mustard, olive oil, lemon juice, salt and pepper. Whisk until completely combined.
Finishing the salad.
Dump the grilled potatoes into the mixing bowl with the vinaigrette, and then toss to coat. Add the capers, parsley, dill, chives, and thyme, tossing in the vinaigrette one last time. Adjust seasoning with salt and black pepper, as needed. Serve immediately or transfer to the fridge and enjoy within 5 days.