1. Preheat oven to 400.
2. Cut 4 russet potatoes into very thin slices, about 1/8-inch thick. I like to use a mandolin for this, but a nice, sharp knife (and some patience!) work too. Just get them as thin as you possibly can. Put the potatoes in a large bowl, separating any big clumps of slices (it happens, you'll see).
3. In a small bowl, whisk together 5 tablespoons olive oil, 1 tablespoon tomato paste, 1 tablespoon salt, 2 teaspoons smoked paprika, 2 teaspoons garlic powder, 1 teaspoon dried thyme and 1/2 teaspoon cayenne powder. Pour mixture over potatoes and toss well to ensure all the potatoes slices are coated in oil and seasoned well. I like to just get in there and use my hands for this.
4. Grease your muffin tin, if needed (see note below). Layer the potatoes in each tin, pressing and stacking all the way to the top. The stacks will shrink as they roast, so fill them way up! Don't worry if you have slices that are not perfect circles (I tend to have a bunch of random half-moons even when I use a mandolin), just stack them like normal. You can also put those smaller pieces around the side. Brush each stack with a little extra olive oil.
5. Cover pan with foil and roast for 20 minutes. Remove foil and roast for another 25-30 minutes, until the tops and sides look extra crispy and a toothpick, cake tester or butter knife slides in easily in the center. Because of the seasoning, these might look a little extra-brown early on, but make sure to roast them fully!
6. While potatoes roast, combine 1/2 cup mayo with the remaining 1 tablespoon olive oil, 2 grated or minced garlic cloves and 1 teaspoon lemon juice. Add a pinch of salt and mix to combine. Keep in the fridge until needed. 
7. When potatoes are done, run a butter knife around the edges and gently remove from tin. Sprinkle with a little flaky salt, if desired, and serve immediately with garlic-mayo.

Recipe and technique inspired by Half Baked Harvest.