Strip the leaves from sharpest end of the rosemary sprigs, leaving a few at the top, making enough for 12 skewers. Alternatively, you can use short, soaked bamboo skewers. Thread 3 mushrooms onto each skewer.
Finely chop the garlic and 1 tbsp of the rosemary leaves together on a board. Heat 2 tsp oil in a large frying pan over medium heat. Lightly toast the garlic and rosemary mixture for 1 minute or until lightly golden. Remove and combine with the lemon zest in a bowl.
Increase the heat to medium-high. Melt the butter and remaining oil in the pan. Cook the mushrooms skewers for 4 minutes each side or until golden and cooked. Season to taste with salt and pepper. Transfer to a platter and scatter over the gremolata to serve.