Cut open the pumpkin by cutting a circle around the stem end with a sharp knife and pulling off the top.
Use a strong metal spoon to scrape the insides of the pumpkin and scoop out the seeds and strings.
Place the mass of pumpkin seeds in a colander and run under water to rinse and separate the seeds from everything else.
Measure the pumpkin seeds in a cup measure. Place the seeds in a medium saucepan. Add 2 cups of water and 1 tablespoon of salt to the pan for every ½ cup of pumpkin seeds.
Bring the salted water and pumpkin seeds to a boil. Let simmer for 10 minutes. Remove from heat and drain.
Preheat the oven to 400°F. Coat the bottom of a roasting pan or thick baking sheet with olive oil.
Spread the seeds out over the roasting pan in a single layer, and toss them a bit to coat them with the oil on the pan.
Bake on the top rack until the seeds begin to brown, 5 to 20 minutes, depending on the size of the seeds.
When lightly browned, remove the pan from the oven and let cool on a rack.
