In a small saucepan, bring 1 quart of water to a boil. Add 1 teaspoon of salt and the eggs (still in shells) and simmer over moderately high heat for 5 minutes. Using a slotted spoon, transfer the eggs to a bowl of cold water and let stand for 3 to 4 minutes. Keep the pan of hot water on the stove over low heat.
Meanwhile, put the spinach in a large bowl. In a medium skillet, combine the olive oil, cider and balsamic vinegars, shallots and thyme, and boil for 1 minute.
Crack the eggs all over and gently peel them under warm running water, keeping them whole. Using a slotted spoon, slip the eggs in the hot water (reserved from earlier) for 30 seconds.
Pour the warm dressing over the spinach, season with salt and pepper and toss. Mound the salad on plates, top each with an egg and serve.