Put quartered figs into a bowl and pour in enough water to cover them completely. Cover bowl and place in refrigerator to soak for 12 hours.
After 12 hours, pour figs and soaking water into a medium saucepan. Simmer over low heat for 2 1/2 hours, adding more water as necessary to prevent figs from becoming dry.
Preheat oven to 350 degrees F (175 degrees C).
To Make Fig Filling: In a small bowl, combine 2 beaten eggs, 2 tablespoons sugar, and salt. Blend together. Gradually pour hot fig mixture into beaten eggs, whisking constantly. Return filling mixture to saucepan. Cook over low heat, stirring constantly, until mixture thickens. Pour fig filling into baked pie shell.
To Make Meringue: In a medium mixing bowl, beat 3 egg whites until foamy. Continue to beat while adding 1/4 cup sugar one tablespoon at a time, until whites form stiff peaks. Spread over fig filling, sealing completely to edge of crust.
Place in preheated oven and bake 10 to 12 minutes, until meringue is browned.