Purée blueberries in a blender or food processor until smooth—strain the juice through a fine-mesh strainer to equal 2 cups; add a little water if necessary. Whisk together the sugar, cornstarch and salt. Whisk in the blueberry juice; bring to a boil in a medium saucepan, whisking. Cook for 1 minute.

Place yolks in a bowl; gradually whisk in half of hot juice mixture. Return to pan. Cook over medium heat, whisking, until thick, about 1 minute. Whisk in butter. Pour into cooled pie shell and refrigerate until set, at least 4 hours or overnight.

Preheat broiler with rack about 8 inches from heat source. Heat egg whites and remaining ¾ cup sugar in a double boiler or a heatproof bowl set over a pan of simmering water, whisking, until sugar dissolves and mixture is hot (160°), about 2 minutes. Transfer to the bowl of a mixer. Whisk on high speed until medium peaks form. Dollop the meringue onto the chilled pie. Broil until lightly browned, 30 to 40 seconds.