Add cranberries, 1 cup granulated sugar, and ¼ cup water to a saucepan over medium-high heat. Bring up to a boil, then reduce to a simmer and cook until the berries burst open and the mixture thickens, about 15-20 minutes. The texture should resemble cranberry sauce.
Puree in the food processor (or blender) until it's as smooth as possible. This may take a good 3-4 minutes. *Use caution blending hot liquids.
Add the eggs, egg yolks, Meyer lemon zest (or orange/lemon zest), Meyer lemon juice (or orange/lemon juice), salt, and remaining ½ cup sugar to the food processor and pulse a few times to combine.
Scrape the mixture into a heatproof bowl set over a saucepan of simmering water (don't let the bowl touch the water) at about medium heat. Stir the mixture constantly with a rubber spatula until it thickens up like a curd and nicely coats the back of a spoon, about 15-20 minutes, or until a candy thermometer reaches 165 degrees. Don't rush this step - it's essential to getting the filling to set up.
Remove the pan from the heat. Set a fine meshed strainer over a bowl, then pour the curd through. Press with a rubber spatula to make sure you get as much of the curd through as possible while leaving the bits of cranberry skin and coagulated egg in the strainer. Let cool until just barely warm.
Beat the curd with an electric mixer on medium-high speed, adding softened (very important) butter one piece at a time. Be sure each piece of butter is fully incorporated before adding in the next.
Continue beating the curd until all of the butter has been incorporated and it looks a few shades lighter in color, about 6 minutes.
Pour the curd into the prepared crust and smooth out the top. Gently bang the pie dish on the counter to remove any air bubbles, then chill until firm, at least 8 hours or overnight is best.
Pie can be made 2 days ahead. Cover and keep chilled until ready to serve.