In a heatproof bowl set in the microwave, partially melt the butter. Add the peanut butter and warm it for another 30 seconds until it’s all soft enough to whisk.
Add the brown sugar, granulated sugar, salt, soda and vanilla and whisk very well - for about 3 full minutes.
Add the egg and yolk and whisk for another minute. Add the flour and whisk until just half of it is mixed in. Switch to a rubber spatula and add the milk chocolate and mix to fully combine. Don't cover the bowl but stick it in the fridge for an hour or two (if leaving for longer than 2 hours, cover it with plastic wrap).
Preheat the oven to 350 F. Line two greased baking sheets with parchment paper.
In a small bowl combine 3 tablespoons granulated sugar with a pinch of fine sea salt.
Scoop rounds of cookie dough, about 3 tablespoons each onto the prepared cookie sheet. As you scoop, dip them face down into the sugar & salt mixture.
Bake the cookies for about 13 minutes, until they are golden around the edges. They won’t spread much but they’ll dome.
As soon as you take the tray out of the oven, use the back of a measuring cup to gently but firmly press down on the cookies into an even layer. Let cookies cool for a few minutes before transferring off the cookie sheet.
Store in an airtight container. Cookies keep well for about 3 days.