Step 1: Whisk eggs, 1/2 cup sugar, and salt in a heavy saucepan until slightly thick. Whisk in buttermilk. Cook over medium-low heat, stirring constantly, until the mixture coats a metal spoon and reaches 165 degrees F, about 10 minutes. Set the pan in a bowl of ice water and stir until cooled. Stir in yogurt. Refrigerate for 8 to 24 hours.
Step 2: Meanwhile, combine blueberries, the remaining 1/4 cup sugar, and lemon juice in a small saucepan. Bring to a boil over medium-high heat, whisking frequently. Reduce heat and simmer until syrupy, about 5 minutes. Let cool. Transfer to a bowl and refrigerate for 8 to 24 hours.
Step 3: Freeze the chilled buttermilk mixture in a 1 1/2- or 2-qt. ice cream maker according to manufacturer’s directions. Transfer to a freezer container. Swirl in the blueberry mixture. Freeze until firm, 6 to 8 hours.
Step 4: Let stand at room temperature for 20 to 30 minutes before serving. Garnish with fresh blueberries and mint, if desired.