In a medium nonstick sauté pan, melt butter and olive oil over medium-high heat. Add onion. Cook until onion is tender and very light brown, 10 to 15 minutes, stirring occasionally. Let onion cool completely.
Using a sharp knife, finely chop onion.
In a small bowl, combine onion, mayonnaise, lime zest, lime juice, salt, and pepper, stirring well. Cover and refrigerate until needed, up to a day.
Recipe by TeaTime Magazine at https://teatimemagazine.com/beef-spinach-sourdough-tea-sandwiches-recipe/