Engine starts but then it stalls

I have a weird problem. When starting the engine after driving it for an hour, the engine starts but then it stalls. For example, after work, I drive home. No problem starting the car at work. When I get home, I turn off the engine. After 20 - 30 minutes, I start the car again. This time, it seems like it's having a hard time to start. It sputters and sometimes it dies. When it dies, I try to start again and it starts. At this point, I can hear cranking sounds in the engine. I am able to drive fine, and no problem with stopping the car. It's just that I hear that weird sound.

I have no problem starting the car in the morning.

Again, this problem only occurs when I start the car 20 - 30 minutes after I've driven for a long time (an hour, 35 km).

I had my alternator and battery changed a year ago. The engine light is on.

Any ideas on what could be causing this?

Thanks!