Bring a medium sauce pot of generously salted water to a boil. Separate the spaghetti so the noodles don’t clump together during cooking. Add the spaghetti and cook, stirring occasionally, until just tender, 3 to 5 minutes. Drain the spaghetti, reserving ½ cup [⅔ cup] pasta cooking water.
While the water heats and the spaghetti cooks, prepare the vegetables and panko.

• Remove any coarse stems from the dandelion greens; coarsely chop the leaves.
• Peel and coarsely chop the shallots.
• Finely chop, press, or grate enough garlic to measure 1 teaspoon [2 tsp].
• In a small bowl, stir together the panko and 1 teaspoon [2 tsp] pepper; season to taste with salt. Set aside for garnish.

In a large frying pan over medium-high heat, warm 1 to 2 teaspoons oil until hot but not smoking. Add the greens and shallots (the greens in batches if needed), season with salt and pepper, and cook, stirring occasionally, until starting to soften, 2 to 3 minutes. Stir in the garlic and as many chile flakes as you like and cook until fragrant, about 1 minute. Transfer to a plate. Do not clean the pan.

• Set aside half the Parmesan for garnish.

In the same pan used for the vegetables, warm 1 to 2 teaspoons butter or oil over high heat until hot but not smoking. Crack the eggs directly into the pan and season with salt and pepper. Cook until the whites are set and crisp and the yolks are slightly runny, 2 to 3 minutes. Reduce the heat to medium and add the spaghetti, vegetables, 2 tablespoons [¼ cup] oil, half the Parmesan, and half the reserved pasta cooking water. Break up the eggs as you stir. Add more cooking water if needed to reach the desired consistency. Remove from the heat and season to taste with salt and pepper.

Transfer the spaghetti to individual bowls. Garnish with the panko, remaining Parmesan, and any remaining chile flakes, if desired, and serve.