Scrub the potato (or potatoes) using a stiff brush, and rinse under cool water. Dry the potato with a clean towel. Look over the cleaned potatoes, and remove any eyes (the part where the plant grows out), bruises, or discolored spots. Drizzle oil over potato and sprinkle with salt. Rub the oil and salt all over the potato using your hands so that the whole potato is lightly coated with oil and salt. Pierce each potato with a fork or sharp knife several times; this will allow moisture to escape during the baking.
Potato Oven Method: Preheat oven to 350° F, and position oven rack in the middle. Place prepared potato on a cookie sheet or large baking dish and bake until tender when pierced with a fork, about 60 minutes.
Potato Grill Method: Preheat the grill to medium-high. Wrap potatoes in foil. Place potatoes on grill grates and cook with the lid down for 45-60 minutes, or until the potatoes are tender when pierced with a fork or knife.
Grilled Onions: While to potato bakes, prepare the onion. Peel the onion. Slice the onion in thick slices going across the circular grain so that you have rings.
Onion Stove-top: preheat a grill pan over medium-high heat. Add a small amount of oil, about a teaspoon. Place onion slice in hot pan and cook until the onion is softened and browned, about 10 minutes. Turn onion and continue to cook until both sides are evenly browned.
Onion Grill: Place onion slices directly on the hot grill and grill until the onion is softened and browned, about 10 minutes. Turn onion and continue to cook until both sides are evenly browned.
Chop onion into smaller, bite-sized pieces. Set aside.
Once the potato is cooked: Cut potato open by cutting a line across the top from end to end with a sharp knife. Then quickly and firmly, smack the potato down on a cutting board or sturdy bowl (this will help fluff up the potato inside creating a hot fluffy potato).
Potato is now ready to be filled. Sprinkle chopped onion, grated Manchego cheese, fresh thyme, and freshly grated pepper into potato. Taste for salt, adjusting as necessary. And, if desired, garnish with a pat of butter.