For the mustard-chive creme fraiche: Whisk together the creme fraiche, mustard and chives in a small bowl and season with salt and pepper.
For the boxty: Preheat the oven to 200 degrees F. Put a cooling rack on a baking sheet.
Cut half of the potatoes into large dice, place in a medium saucepan, salt generously and cover with cold water by 1 inch. Bring to a boil over high heat, reduce the heat to low and simmer, uncovered, until the potatoes are fork-tender, about 10 minutes.
While the potatoes are cooking, grate the remaining potatoes on the large holes of a box grater. Toss with 1/4 teaspoon of salt and then wrap the potatoes in cheesecloth and squeeze very hard to drain out as much liquid as possible.
Put the milk, flour, baking powder, egg, 1 teaspoon salt and 1/8 teaspoon pepper in a large bowl and whisk until smooth.
Drain the boiled potatoes and return them to the pan. Add the half-and-half and 3 tablespoons of the butter and mash until the potatoes are smooth. Give the grated potatoes one final squeeze and then stir them into the mashed potatoes. Stir the potato mixture into the milk-egg mixture.
Heat a large nonstick or cast-iron skillet or griddle over medium heat. Add a few tablespoons of canola oil and some of the remaining butter and cook until beginning to shimmer. Working in batches, drop scant 1/4 cups of the batter into the skillet and shake the skillet to spread the batter into 1/4-inch-thick rounds. Cook until the pancake bottoms are golden brown, 3 to 4 minutes. Flip and cook the other side until golden brown, about 2 minutes longer. Transfer to the prepared baking sheet and keep warm in the oven while you repeat with more oil, butter and batter.
Serve the potato pancakes warm, topped with a dollop of the mustard-chive creme fraiche, slices of salmon and some chives.