Prepare the dressing by combining the creme fraiche and grainy mustard in a bowl. Add a bit of salt and freshly ground pepper. Now, add just enough water to thin the mixture so that it can drop from a spoon, about 1 Tbsp. or a bit more, if needed. Cover and refrigerate until needed.
Prepare the potatoes by cutting lengthwise into 1/4-inch slices, discarding the rounded outside slices. Bring a large pot of salted water to a boil, then add the potato slices and boil until just tender, about 8-10 minutes. Drain, then remove the slices to an even layer on a baking sheet. Brush top side of the potato slices with olive oil and sprinkle with salt and pepper.
Heat BBQ or grill pan to high heat. Place slices on the grill, oiled side down and cook until lightly charred, on the underside, about 5 minutes. Before flipping, brush the top side of the potatoes with more oil and sprinkle with salt and pepper. Flip potatoes and cook the other side until lightly charred, a further 5 minutes.
Remove potatoes to a cutting board. Slice in half lengthwise and toss into a serving bowl or skillet. Sprinkle with a bit more salt and pepper. Drizzle with creme fraiche dressing and garnish with chopped fresh dill.
NOTE: How to Make Creme Fraiche at Home: In a medium jar, stir together 1 cup of heavy, 35% whipping cream (not ultra-pasteurized) and 1 Tbsp. buttermilk. Set a lid on top, but don't twist to seal it (to allow air to escape, but to keep dust and things out). Set on your counter or window sill for 12-24 hours, or until the mixture resembles stirred sour cream. The time it takes to that point will vary depending on the temperature of your room. Mine took about 20 hours. At that point stir the mixture well, then transfer to the fridge, again, topping with a lid but not twisting to seal it, as it will continue to process). Refrigerate a further 6 hours or longer, or until it is the consistency of cream cheese.