Position a rack in the center of the oven and heat the oven to 425°F. Butter a 9x13-inch (or similar) baking dish.
On a large, rimmed baking sheet, toss the fennel with 2 Tbs. of the oil, the vinegar, 1 tsp. salt, and 1/4 tsp. pepper. Spread in a single layer and roast, stirring once or twice, until golden-brown, about 35 minutes. Transfer to the prepared dish. Reduce the oven temperature to 350°F.
In a 12-inch skillet, melt 1 Tbs. of the butter and the remaining 1 Tbs. oil over medium heat. Add the onion, bay leaves, 1 tsp. salt, and 1/4 tsp. pepper and cook, stirring occasionally, until golden, 8 to 10 minutes.
Meanwhile, melt the remaining 2
Tbs. butter and pour into a medium bowl. Add the breadcrumbs, Parmigiano Reggiano, and 2 Tbs. of the fennel fronds and toss well.
Add the Pernod to the skillet, scraping up any browned bits, and continue to cook until most of the liquid has evaporated, about 1 minute. Stir in the heavy cream, the remaining 2 Tbs. fennel fronds, 1/2 tsp. salt, and 1/4 tsp. pepper and bring just to a boil. Reduce the heat to medium low and simmer for 5 minutes to infuse; discard the bay leaves.
Spoon the cream mixture over the fennel, scatter the breadcrumb mixture over the top, and bake until the fennel is tender when pierced with a fork and the breadcrumbs are browned, about 30 minutes.
Let rest for 10 to 15 minutes before serving.