Add the potatoes to a large saucepan or Dutch oven, then cover with cold water and sprinkle with 2 tablespoons kosher salt. Place over medium-high heat and bring to a boil, then reduce to a simmer. Cook until the potatoes are tender, 6 to 7 minutes.
Meanwhile, add the watercress, vinegar, honey, mustard, paprika and 1/4 cup olive oil to the bowl of a food processor or mini chop. Process until very finely chopped. Set aside.
Preheat a grill or grill pan to medium-high heat.
Drain the potatoes and run cold water over them to cool. Slice in half lengthwise and place in a large bowl. Drizzle the potatoes with the remaining 3 tablespoons oil and sprinkle with 1/2 teaspoon each of salt and pepper.
Add the potatoes, cut-side down, to the grill and cook until the potatoes are slightly charred and have grill marks, 2 to 3 minutes per side. Place cut-side up on a serving platter. Spoon about 1/2 teaspoon of the watercress mixture on each potato. Serve warm or at room temperature.