Place the strawberries, rhubarb, 2 tablespoons sugar and 2 tablespoons water in a medium-sized saucepan set over medium heat. Cook for approximately 10 minutes, stirring occasionally, optionally mashing with a potato masher to help extract juices. The mixture is ready when the rhubarb is soft.
Cool for 5 minutes, then puree in blender until smooth.
In a medium saucepan, whisk together the egg yolks and sugar until smooth, thick, and pale yellow. This will take around 30 seconds. Whisk in the milk, cream, salt and vanilla until evenly combined.
Place the saucepan over medium heat. Whisking almost constantly, cook the mixture until an instant-read thermometer reads 170 degrees F, approximately 10 minutes.
Strain the gelato base through a fine mesh strainer into a medium-size bowl, preferably one with a pouring spout. Whisk in the strawberry rhubarb puree until smooth (note: you can add the puree to the base before straining if you want to ensure a totally smooth gelato, but I think the strawberry seeds and occasional bits of rhubarb add a nice texture).
Place plastic wrap directly against the surface of the liquid to prevent a skin from forming. Chill until the mixture is very cold, at least 6 hours or up to two days in advance.
Briefly whisk the mixture, then prepare in an ice cream maker according to manufacturer instructions.
Once the gelato has finished spinning, it will likely be a soft serve consistency. Transfer to a loaf pan (or similar sized pan), cover, and freeze until fully frozen but scoopable, up to 2 hours.
Enjoy within 1-2 weeks for best flavor and texture. If the gelato is too firm to scoop directly out of the freezer, let it sit on the counter or in the refrigerator for 5 minutes before serving.