Starting and then restarting

Possible heat soak issue causing fuel vaporization. Try opening the hood as soon as you shut it down which may vent enough heat out to prevent this problem. You may need to reroute your fuel lines away from heat. Does your choke have a "hot" or "warm" setting?

I had a 1070 MGB Roadster that displayed a similar problem and discovered a faulty fuel pump. The valve that prevented back flow into the pump broke and a circular part of the valve was loose in the fuel line. When ever it moved to a position perpendicular to the fuel line, it would cut off fuel flow shutting down the engine, sometimes at highway speed. When the engine was shut off, the pressure on the loose part was released and the disc fell over, allowing fuel to flow. I discovered this the morning that I sold it. When the engine shut down on me one more time, I pulled off the fuel line to the carburetors (again)because the car would not continue running. The round piece of plastic had worked its way up to the carburetors sometimes going with the flow and sometimes blocking it. When I removed the fuel line it popped out into my hand.