This is almost certainly not fuel starvation, but flooding due to percolation: when you stop the engine, the radiator fan is no longer blowing air past the carburetor and manifolds. Heat rises and the carburetor becomes a tea kettle. Today's fuels have a lower boiling point than the fuels of the past, which is no problem with closed pressurized fuel systems (fuel injection) but makes a problem with open systems and carburetors. The fuel boils in the carburetor and collects in the intake manifold. When you come back and try to start the car, it takes a lot of cranking to clear out the overload of fuel before the mixture in the cylinders is lean enough to be combustible.
Solutions start with the dead simple: use the correct starting procedure. When the engine is hot, hold the accelerator about 1/3 of the way down (don't pump it!) while cranking. In extreme cases of percolation flooding, with the engine spluttering and "trying" to start, hold the accelerator all the way to the floor while cranking. Either action holds the throttle partly or fully open to admit more air to the intake tract and speed the clearout of accumulated fuel.
Make sure the correct carburetor base (mount) gasket is in place. It should be a 3/8" thick insulator block.
Make a heat shield for the carburetor. This is to be sandwiched between the carburetor and the carb mount gasket. Make it of 1/16" semi-rigid gasket material. Copy all the holes and notches in the carb mount gasket. There used to be such a shield available from the factory, but it is long discontinued. By looking at the picture, you can see that it should extend several inches forward, rightward, and leftward of the carburetor mount axis. The factory shield was a 2-piece item; the rearmost part is nowhere near as critical as the front/side coverage:
Go through and rebuild the carburetor with a quality kit (such as from
www.daytonaparts.com ; their kits also usually have a better inlet needle/seat assembly more resistant to flooding), and install a new float, Walker number 100-14 (Daytona should also have a new float for this carburetor; ask them). Carburetor operation and repair manuals and links to training movies and carb repair/modification threads are posted
here for free download.