How can I roast melon seeds, without oven or too much oil? My mom lives Hong Kong when Toronto's cold. Here are strictures:


Healthy frying is OK. But NO deep-frying.
Her HK flat doesn't have a convection oven. She never bought microwave oven.
She could buy a counter-top convection toaster oven, but she feels it's too eco-unfriendly and waste of money. Let's rule it out for now. 
If nobody comes up  anything, she will reconsider.  She has a rice cooker. Her kitchen looks like




This Salon.com article recommends roasting honeydew and cantaloupe seeds. My mom wants to roast seeds in pricey Japanese melons.
I've sometimes toasted pumpkin seeds (very similar) in an enamelled cast iron frying pan. I don't add oil to the pan, but the seeds are better if you mix a little oil with them, especially if you want spices to stick. In that case stir about a teaspoon of oil (olive, sunflower etc.) into a generous handful of seeds, add any spices/salt, put into a preheated pan, and stir frequently until they're done. 

I wouldn't use non stick for this because a dry pan can get very hot in places, perhaps too hot, but bare stainless steel  also works.

This stove top method is quicker than an oven especially if you only want a small batch, but it's more important to start with the seeds nicely dry than if you're using an oven. It probably uses more electricity than a toaster oven though.