1 tablespoon olive oil, divided
1 (10-ounce) bag baby spinach, chopped
3 garlic cloves, minced
3 vertically sliced shallots
1 tablespoon chopped fresh sage
3/4 teaspoon chopped thyme, divided
1/2 teaspoon black pepper, divided
1/4 teaspoon salt
1 (8-ounce) package cremini mushrooms, quartered
3/4 cup toasted walnuts, chopped and divided
2 tablespoons red wine vinegar
2 ounces shredded Gruyere cheese
8 cups water
2 tablespoons white vinegar
4 large eggs