Set up and pre-chill the ice cream maker. Prepare the ice bath by placing a 2-quart (2l) bowl in a larger bowl partially filled with ice and water. Set a strainer over the top of the smaller bowl. .
Whisk together the egg yolks, sugar, and miso.
To make the ice cream custard, heat the milk and heavy cream in a saucepan. Gradually pour some of the warm milk and heavy cream mixture into the yolks, whisking constantly as you pour. This technique is called “temper.” It prevents you from making scrambled eggs in your ice cream custard. Scrape the warmed yolks with miso and milk back into the saucepan.
Cook over low heat, stirring constantly and scraping the bottom with a heat-resistant spatula until the custard thickens enough to coat the spatula. It should be 170 F to 175F on an instant-read thermometer. Do not allow the custard to boil. Strain the custard through a fine-mesh strainer into the smaller bowl and stir over the ice until cool.
Using an immersion blender, puree the strawberries with the lemon juice and stir into the ice cream base. Add the vanilla extract.
Cover the ice cream base with plastic wrap. Add applewood chips to the burn chamber of the Breville Smoking Gun. Place the hose under plastic wrap with the opening sitting above the custard. Seal the plastic wrap.
Turn the smoking gun on to HIGH SPEED and ignite woodchips. Switch to LOW SPEED and smoke for a few seconds until the bowl is filled with a dense smoke. Remove the hose and reseal the plastic wrap. Let it infuse in the refrigerator for 5~10 minutes. Taste the ice cream base. If it’s not smoky enough, repeat the smoking process one more time, stirring custard between each smoking session.
Refrigerate the ice cream base to chill thoroughly, preferably overnight.
Churn in your ice cream maker according to the manufacturer’s instructions. Enjoy right away or transfer to a freezer-safe container to chill until firm.