Preheat oven to 425 degrees F (220 degrees C). Grease a 12-cup muffin tin or line with paper liners.
Place asparagus in a bowl with a small amount of water; cover and cook in microwave on High, 30 seconds at a time, just until tender. Drain asparagus; set aside to cool.
Whisk flour, marjoram, thyme, baking powder, baking soda, pepper, and salt together in a bowl. Beat egg in a separate bowl; beat in buttermilk, melted butter, and olive oil. Stir Cheddar cheese, green onions, capers, and asparagus into buttermilk mixture.
Stir buttermilk mixture into flour mixture just until dry ingredients are moistened; spoon mixture into prepared muffin cups 2/3 full.
Bake in the preheated oven until a toothpick inserted near the center comes out clean, about 15 minutes. Cool on a wire rack for a few minutes; serve warm.
