Arrange the toasted muffins cut side up on a work surface.
In a small bowl, mix together the mayonnaise and Sriracha. Slather the cut sides of the muffins with the mayo mixture.
Divide the arugula among the bottom halves of the muffins. Arrange the avocado and radish slices on the top half of the muffins.
In a nonstick skillet or on a griddle, melt the butter over medium heat. Crack the eggs (working in batches if needed) into the skillet, and using the corner of the spatula, break the yolk. Cook, turning once, until the eggs are just set, 2 to 3 minutes.
Season the eggs with salt and pepper and transfer to the bottom sides of the muffins. Close the sandwiches and serve.