Preheat oven to 350.
Line an 11x17 inch jelly-roll pan or two 9 inch square pans with nonstick foil.
In a medium size bowl, thoroughly mix together the flour, cocoa powder, salt and baking soda.
In a large mixing bowl using a handheld electric mixer, beat the eggs and sugar for about a minute. Beat in the chocolate syrup, vanilla extract and butter until mixture turns light brown. With a heavy rubber scraper or a spoon, stir in the flour mixture until incorporated.
Pour batter into lined pan and bake 10-12 minutes or until cakes seem firm and set. Remove from oven and let cool completely. Lift from pan and set cookie on a large cutting board.
Cut the cookie lengthwise to make two long rectangles, then cut cross-wise to make 4 rectangles (this makes them easier to work with). Place one of the rectangles on a big sheet of plastic wrap and spoon ice cream evenly over the top. Cover with second rectangle and press down slightly. Wrap tightly in plastic. Repeat with second set of rectangles. Set on a baking sheet and put in the freezer overnight or until very firm.
Using a large knife, trim the sides to give the sandwiches a clean edge. Cut each section into 4 rectangles.