Add broccoli, onions and garlic to pan. Drizzle with olive oil. Sprinkle with salt and pepper. Toss with clean hands, until coated. Wiggle the pan until broccoli is in a single layer. Bake 20-25 minutes until fork tender.
Grease a 10″ bundt pan with butter or shortening very liberally. Dust the pan with flour and set aside.
Place all the cake ingredients in the bowl of your stand mixer fitted with the paddle attachment. Mix on low for 30 seconds and then increase the speed to medium and mix for 3 minutes.
Pour the batter into the prepared pan and bake for 65-75 minutes until a toothpick entered into the center comes out clean.
When the cake is done make the glaze. Combine all ingredients into a small saucepan over medium-low heat. Stir continuously until the butter is melted and the sugar is dissolved. Do not bring to a boil.
Poke holes all over the warm cake using a knife and pour the glaze evenly on the cake while still in the pan.
Allow the cake to cool completely in the pan and then invert the cake onto a serving plate.
Make this cake a day in advance, it wil be more moist and flavorful when it rests overnight.