Heat 1 tablespoon oil in a large saute pan over medium heat. Add spinach and cook, tossing occasionally, until wilted and starting to look dry, about 5 minutes. Transfer spinach to paper towels, and squeeze out excess liquid.
Place spinach and mayonnaise in a food processor, and blend until very smooth. Pass through a fine sieve, and discard solids. In a clean food processor bowl, pulse spinach mixture, mustard, yolks, and remaining 1 tablespoon oil. Add salt and pepper, and pulse to combine.
Transfer mixture to a large piping bag fitted with a 1/2-inch star tip, and pipe filling into each egg-white half. Alternatively, spoon filling into whites. Garnish each with a small sprig of chervil or thyme, and serve immediately.