Steak and Fennel Croissant Sandwiches

Name: Steak and Fennel Croissant Sandwiches
Ingredients: 1⁄2 teaspoon fennel seed, ground; 1⁄2 teaspoon salt; 1⁄4 teaspoon cumin; 1⁄4 teaspoon black pepper; 4 teaspoons olive oil, divided; 3 cups fennel, thinly sliced, about 1 bulb; 16 ounces beef tenderloin steaks, about 1-inch thick; 8 teaspoons homemade mayonnaise, recipe follows; 4 croissants, split in half and lightly toasted; 1 cup arugula; Homemade Mayonnaise; 1 tablespoon fresh lemon juice; 1⁄2 teaspoon Dijon mustard; 1⁄8 teaspoon salt; 1 egg; 3⁄4 cup oil