Preheat the broiler. Set the rack near the top of the oven so that the top of the frittata will be 5 to 6 inches from the heat source.
Snap the tough ends off of the asparagus spears and cut diagonally into 1-inch pieces. Separate the tips from the other pieces.
Heat olive oil in a 10-inch nonstick, ovenproof skillet set over medium heat (you can also use a cast-iron pan, but you may experience more problems with the frittata sticking to the pan). Add the onions to the skillet and cook, stirring occasionally, until the onions are beginning to soften, 3 to 4 minutes. Add the asparagus stalk pieces (not the tips) ¼ teaspoon salt, and ¼ teaspoon freshly ground black pepper to the pan and cook until the asparagus pieces are tender-crisp, about 3 minutes (more time may be needed if you are using thick asparagus spears). Add the asparagus tips and cook for an additional 2 minutes.
While the onions and asparagus are cooking, whisk together eggs, smoked paprika, and thyme in a large bowl. Slowly pour the egg mixture over the onions and asparagus. Stir slightly to evenly distribute the vegetables. Turn the heat down to medium-low. Season with ¼ teaspoon salt and ¼ teaspoon freshly ground black pepper. As the eggs are cooking, run a rubber spatula around the outside of the frittata to release the eggs from the pan. When about half of the egg mixture is set and the bottom of the frittata is golden brown, sprinkle feta cheese over the top of the frittata. Place the frittata under the broiler and cook until the frittata is slightly puffed and golden brown, about 3 minutes. Remove from the oven.
Using a rubber spatula, slide the frittata from the skillet onto a serving platter. Cut into 4 wedges and serve immediately. If you are not able to easily slide the frittata from your pan, cut it into wedges in the pan and gently lift out each wedge.