Preheat oven to 385°F. Spray a 9"x13" pan generously with nonstick cooking spray or grease with butter and set aside.
In a food processor (or in a large bowl with a pastry cutter), add in the sugar, flour, salt, and baking powder. Pulse until well mixed.
After pulsed, add in cubes of butter and pulse well until butter is dispersed throughout and mixture is crumbly. (Or use butter knives or a pastry cutter to cut the butter into the flour mixture until crumbly.)
Add mixture to a large bowl and add in eggs (whisked), plus cream, and vanilla. Mix well. The dough will be very tacky! Mix with hands or a rubber spatula until well combined.
Using wet hands, scoop the dough into the prepared pan. It will tacky! Use hands or a rubber spatula to pat dough into pan. Try to spread it as evenly as possible.
Sprinkle the coarse cane sugar or crystalized sugar over the top of the dough. This will give the top a great sugary crunch after baking.
Place into preheated oven and bake for 35-45 minutes until top and sides are golden brown and the middle of the shortcake springs back to the touch.
Once done, remove from oven and set on stovetop to cool in pan.