Save baby spinach for salads -- for this recipe, a heartier variety is best. Look for leaves that are thick and curly, which will retain more texture and flavor when sauteed.
Heat a large skillet over medium. Add pepitas and toast, shaking pan occasionally, until they begin to swell and darken slightly, about 2 minutes. Add sesame seeds and continue toasting until pepitas and sesame seeds turn golden brown in places, about 1 minute more. Transfer to a plate; let cool completely.
Return skillet to medium-high; swirl in 2 tablespoons oil. Add garlic and ginger, season with salt, and cook until fragrant, about 30 seconds. Add enough spinach to fill skillet. Cook, stirring, until spinach begins to collapse. Add remaining spinach, a handful at a time, until all is just wilted. Stir in vinegar and cook 30 seconds. Remove from heat. Stir in remaining1 tablespoon oil; season with salt and pepper. Sprinkle with toasted pepitas and sesame seeds just before serving.