Heat your oven to 425˚F. Slightly trim the ends from the Brussels sprouts and slice in half. Place on a sheet tray and toss with the minced garlic, olive oil, and salt. Place in the oven and roast until tender; 20 to 25 minutes.
While the Brussels sprouts are roasting, make the breadcrumbs. Heat a small pan over medium heat. Add the olive oil, followed by the fennel seeds. Toast the seeds for a minute or two, just until fragrant. Stir in the breadcrumbs and continue to cook/toast until the breadcrumbs are golden. Turn off the heat and add in the lemon zest.
Next, bring a pot of water to a boil. Add in the eggs and keep at a low boil. Cook the eggs for exactly 6 ½ minutes. Transfer the eggs directly to an bowl filled with ice water and let rest until the Brussels sprouts are done.
When the Brussels sprouts are tender, transfer to a serving tray and toss with half the breadcrumbs. Crack, peel, and then slice the eggs in half. Nestle into the Brussels sprouts and top with more breadcrumbs before serving.