Melt butter in a large skillet over medium heat. Add nuts and dates and cook, stirring frequently, until dates are brown and fragrant, 3–5 minutes.
Scrape mixture to a medium bowl and let cool to room temperature (or pop it in the fridge/freezer for quicker cooling).
In bowl of a stand mixer fitted with paddle attachment beat butter, brown sugar, granulated sugar and miso on medium speed until smooth, about 2 minutes, stopping and scraping down sides of bowl a few times.
Add ½ teaspoon minced lemon zest and vanilla and beat to combine. Add egg and mix on medium-high speed until pale in color and fluffy, about 30 seconds.
In a medium bowl, combine oats, flour, baking soda and salt.
Add flour mixture and mix on low speed to combine, about 30 seconds. Add date-nut mixture and mix to combine.
Press a piece of plastic wrap against dough and chill until firm, 30 minutes–1 hour.
Heat oven to 375ºF (190ºC) with rack set in middle position; line a baking sheet with parchment paper.
Using a #24 scoop (50g or 2 ½ tablespoons), scoop dough and arrange 1½ inches apart on prepared sheet pan. Lightly press dough balls to 1-inch thickness.
Bake cookies until edges are set and golden brown, 12–14 minutes, rotating pan halfway through.
Transfer sheet pan to wire rack, sprinkle cookies with flaky sea salt and let cookies cool on sheet pan for 5–10 minutes, or until set enough to easily transfer to rack with hands.