Start by preparing the fennel bulbs. Remove the fennel fronds, chop some up for garnish and set aside, then discard the rest. Slice the bottom root part off and remove any of the rough exterior pieces. Cut each bulb lengthways into 1/2″ thick slices. Set aside. In a large frying pan, melt half the butter and half the oil over high heat.
As the butter starts to foam, add one layer of fennel to the pan. Cook for 2 minutes or until golden brown. With tongs, turn the fennel over and cook for 1-2 minutes until golden. Remove from pan and set aside. Repeat this process until all the fennel is cooked, adding the remaining butter and oil as necessary. Once all the fennel has been cooked, reduce the heat to medium and add the sugar, fennel seed, and a generous amount of salt and pepper to the pan.
Quickly add in all the fennel and caramelize for 1 minute. Remove the fennel from the pan and let it cool to room temperature on a plate. To serve, toss the fennel with the dill and garlic. Taste and season with salt and pepper as necessary. Arrange fennel on a serving platter and dot with goat cheese. Finish with a light drizzle of olive oil and a sprinkling of the lemon zest. Garnish with chopped fennel fronds and serve.