Preheat oven to 350 degrees F (175 degrees C). Spray two 8-inch round cake pans with vegetable oil spray.
In a medium bowl, sift together flour, salt and baking powder. Set aside.
In a large mixing bowl, cream butter with the sugar until fluffy. Add egg and beat well. Add flour mixture alternately with the evaporated milk. Fold in vanilla and almond extracts and 1 cup chopped figs.
Divide into two prepared 8-inch round cake pans. Bake in preheated oven until cake springs back when lightly touched with a fingertip and a toothpick inserted into the center comes out clean, 25 to 30 minutes. Cool cake layers on wire rack.
To make the filling: In a saucepan, combine 2 cups chopped figs, brown sugar, water and lemon juice. Bring to a boil. Reduce heat to a simmer and cook until thickened, about 20 minutes. Spread thinly between cooled cake layers and on top.