Preheat the oven to 350 degrees F. Place a roasting pan on a center rack and fill with 1 inch of water. Leave the roasting pan in the oven while you prepare the filling.
Add the cream cheese to the bowl of an electric mixer fitted with a paddle attachment (or use a hand mixer). Beat the cream cheese on medium speed until creamy, about 2 to 3 minutes. Add the brown sugar, flour and salt. Beat until fluffy, about 2 minutes.
Add vanilla and beat until combined. Add eggs, one at a time, beating just until combined after each addition, being careful not to overmix.
Pour the cheesecake mixture into the prepared pan and smooth over. Tap pan on the counter a few times to remove any air bubbles.
Carefully place the pan in the water in the roasting pan and close the oven door. Immediately reduce heat to 325 degrees F and bake for 70 to 80 minutes, until the middle (center 2-inches) of the cheesecake is still slightly wobbly. Turn off the oven, prop open the door with a wooden spoon and allow to cool for 1 hour.
Remove the cheesecake to a wire rack and run a hot knife around the edges. Continue to cool for 1 to 2 hours, then cover with foil and refrigerate overnight.