Preheat oven to 350 degrees. Butter and flour an 8-inch round cake pan( must be 8 inch pan). In a medium bowl, whisk together flour, salt, baking powder, and baking soda.
With an electric mixer, beat butter and sugar until light and fluffy. Add eggs one at a time, beating after each addition until incorporated; mix in vanilla. With mixer on low speed, alternately add flour mixture in three parts and buttermilk in two, beginning and ending with flour mixture. Mix just until smooth (do not overmix).
Pour batter into prepared pan; smooth top. Bake until a toothpick inserted in center of cake comes out clean, 30 to 40 minutes. Cool 15 minutes in pan; turn cake out onto a rack, and let cool completely. Using a long serrated knife( I use thread or unflavored dental floss as it is easier), halve cake horizontally.
While cake is cooling, combine strawberries and jam in a bowl.
Line sides of a 9-inch springform pan with a strip of waxed paper; wrap outside of pan with plastic wrap. Center bottom half of cake in pan, cut side up.
Spread 1 1/2 pints ice cream over top and down around sides. Spread strawberry mixture on ice cream, leaving a 1-inch border. Set top half of cake over it.
Spread remaining ice cream over top and down around sides of cake. Tap cake on counter to help ice cream settle. Smooth top, and freeze until firm, at least 6 hours or, covered, up to 2 weeks. To serve, remove plastic from pan, unmold cake, and peel off waxed paper. Let cake rest at room temperature for 15 minutes before slicing.