Heat the oven to 450 degrees F. Slice the potatoes on a sharp angle into 3/8-inch slabs. Put them in a colander and rinse (this way you rinse off dirt and lose a little starch for crisper planks). Shake off the excess water and spread them onto a heavy rimmed baking sheet (about 11x18-inches) lined with two layers of paper towels. Cover with a few more paper towels and let dry.

In a medium bowl, combine the olive oil, mustard, rosemary, lemon zest, lemon juice, salt, and pepper; stir until well blended. Dump the dried potato planks into the bowl (discard the paper towels); toss with a spatula until each piece is well coated. Scrape the potatoes onto the same baking sheet and spread in a single layer. Drizzle any remaining herb mixture onto the potatoes.

Bake the planks until browned on the bottom, about 20 minutes, and then flip with a spatula. Continue cooking until they're well browned and tender, about another 15 minutes. Sprinkle with more salt, if you like, and serve immediately.