Preheat oven to 400 degrees F (204 Celsius). Prepare 2 baking sheets lined with parchment paper.Toast bagel and set aside.Divide trimmed green beans between the two baking sheets, spread out into a single layer. Bake for 25-30 minutes. It should look lightly browned with somewhat crisp edges, yet tender on the inside of the beans.Meanwhile, prepare breadcrumbs in a food processor. Combine broken up bagel, italian seasoning, fresh thyme leaves, olive oil, kosher salt, crushed black pepper and pulse until a coarse breadcrumb consistency. Transfer to a bowl and use the food processor for the vinaigrette.To prepare vinaigrette (can make ahead up to 3 days): in a small food processor or by whisk by hand. Combine mayonnaise, extra virgin olive oil, garlic (crushed if whisking by hand), lemon juice, and kosher salt and pulse until well combined.Drizzle vinaigrette on green beans (I combine green beans from both sheets into one) and toss to combine then transfer to your serving dish. Sprinkle on breadcrumbs and extra thyme leaves for garnish and serve.Make ahead: Green beans are freezer friendly when tossed in the vinaigrette only. Thaw at room temperature, then reheat at 300 degrees F (148 Celsius) for 15-20 minutes before adding breadcrumbs. Breadcrumbs can be frozen separately (in a freezer safe container) then assemble before serving.Notes: Each component of this recipe can be made the day before to make holiday baking easier. The breadcrumbs at room temperature will keep them crisp for a couple of days.