Bring a medium sauce pot of generously salted water to a boil. Add the bucatini; cook until tender, 9 to 11 minutes. Drain, reserving ¼ cup of the pasta cooking water.
While the water heats and the bucatini cooks, prepare the eggs.

Bring a small sauce pot of water to a boil; fill a small bowl with ice water. Carefully lower the eggs into the boiling water; cook for exactly 5 minutes for soft-cooked (for hard-cooked eggs, cook for 3 to 4 minutes longer). Transfer the eggs to the ice water to cool. Carefully peel the eggs.
While the eggs cook, prepare the sauce.

• Finely chop, press, or grate enough garlic to measure 1 teaspoon.
• Trim the root ends from the leeks; cut the leeks in half lengthwise, then crosswise into ¼-inch-thick half-moons. Soak the leeks in a medium bowl of cold water, allowing any dirt to settle at the bottom. Skim the leeks from the surface of the water and pat dry.
• Zest and juice enough lemon to measure 1 tablespoon zest and 1 teaspoon juice.
• Remove any pulp from the preserved lemon; finely chop enough peel to measure 1 teaspoon.
• Strip the parsley leaves from the stems; coarsely chop the leaves. Set aside half for garnish.

In a large frying pan over medium heat, warm 1 to 2 tablespoons oil. Stir in the garlic, fennel seeds, and as many chile flakes as you like; cook until fragrant, about 1 minute. Add the leeks; cook, stirring occasionally, until tender, 3 to 5 minutes. Stir in the lemon zest and preserved lemon; cook until fragrant, about 1 minute. Stir in the spinach and reserved pasta water, season with salt and pepper, and cook until the spinach is wilted, about 1 minute.
Stir in the bucatini, lemon juice, panko, and half the parsley; cook until warmed through, 1 to 2 minutes. Season to taste with salt and pepper.

When the sauce is almost done, cut the eggs in half lengthwise.

Transfer the bucatini to individual bowls. Sprinkle with the Pecorino Romano, panko, and remaining parsley, garnish with the eggs, and serve.

Chef's tip: For crisper bread crumbs toast the panko in a dry pan for about 2 to 3 minutes over medium heat.