Combine the marinade ingredients in a bowl and set aside.
Blanch the broccoli in boiling salted water for 2 minutes. Drain and cool.
In a small skillet over medium heat, add the olive oil and cook the garlic cloves until they are golden and soft. Set aside until cool enough to handle.
To make the skewers: Remove the leaves from the bottom 2/3 of the rosemary sprigs and reserve them for future use. Skewer a mushroom, broccoli floret and a roasted garlic clove onto each rosemary sprig. Put the completed skewers on a baking sheet, brush them with the marinade, and season with salt and pepper.
Grill the rosemary skewers over medium-high heat for about 1 1/2 minutes on each side. Serve with a small wedge of Cambozola cheese.