Preheat the oven to 400° F. Toss the potato slices with enough oil to coat them well, plus a big pinch of salt. Once the oven is nice and hot, slide them in. Roast them for about 30 minutes, checking to make sure they don't burn (your cooking time will depend on your potato size, your oven, and whether mercury is in retrograde).
While the potatoes cook, make your sort-of-pesto: First, toast the walnuts on the stovetop until they're toasty. Chop together the mint, sage, and garlic with a pinch of salt, then dump the warm walnuts over them and chop everything together roughly, so you've made a bit of mulch. Transfer to a bowl, then drizzle over some olive oil -- a generous 1/4 cup, maybe, or enough to make this feel like more of a sauce and less of a salad. Add a good splash of sherry vinegar and some pepper, then taste and add whatever you need. Make it nice and acidic. Remember the potatoes will be salty, so don't over-salt it.
Check on your potatoes. When they look almost done, give them a toss, then throw in the capers. Roast for 5 more minutes, until they're good and golden but not burnt, and the capers have started to slouch from the heat.
Put the pesto in a large bowl, then dump the hot potatoes over top, and toss it all together. Finish with some more pepper, or maybe some Parm, or nothing.