Back to finally update my question on Lima, I was able to secure a reservation with Senora Maria Zuniga in this Mark Wiens video. It was worth every bit of 100 soles (US$30) per person. The booking process wasn't quick or easy with lots of back and forth through email and whatsapp and a 70% deposit bank transfer. We had an 8-course lunch, two of them desserts. Her hospitality is as warm and comforting as her food. Oh, and she doesn't speak English and sits down at the table with each course to explain the dish and its cultural foundation. Two thumbs up. ^ ^