My enamel pasta pot, which I've had for years, melted into my solid plate stove after I forgot the plate on. It smelled like burning plastic. I removed the pot and it was so hot that it charred my wooden chopping board. The stove plate was glowing red and after removing the pot there was a residue burnt into the solid plate of my cooker. I tried scraping it off but it had hardened and feels like plastic and looks like solid aluminium. How can I remove the melted parts from the solid plate?
This might not have a happy ending I am afraid. You might need to get a replacement part for the plate.
If it was a true enamel pot (and it sounded like one) rather than an aluminium pot with an anodized surface, that is a metal pot with an enamel coating, once it is heated to above the fusing temperature of the enamel (500C at least, likely much higher), the coating will melt. What you went through is the reverse of the process to apply the enamel.
Enamels are metal based compounds, ceramic or glass like once re-solidified. It tends to fuse with metal and glass with no defined boundary. Despite that it is typically brittle, it is going to be very difficult to get it off the stove, especially if it is a metal hot plate or a ceramic hob. Enamel is pretty unreactive. Anything that would dissolve it would likely first dissolve your cooker surface. It is also much harder than the cooker materials. Heating it back up to fusing temperature would only help enhance bonding of the enamel to the cooker.
Not a terribly helpful answer I am sorry to say. Hopefully, I am wrong and there is a more helpful suggestion from others.