Make the rosemary-infused olive oil: Heat a skillet over medium heat and add the 2 tablespoons extra virgin olive oil over medium heat. Once the oil is shimmering, add the rosemary sprigs. Allow the rosemary to cook for a bit, tossing the sprigs around occasionally, until the oil is bubbling and smells very fragrant, about 2 to 3 minutes. Discard the herbs using a slotted spoon and reserve the oil.
Drain the cashews and rinse with fresh water.
Add the cashews to a high-powered blender or food processor along the rosemary-infused olive oil, garlic, salt, pepper to taste, nutritional yeast, lemon juice, miso, and mustard. Blend on high speed until smooth, thick and creamy, scraping down the sides with a silicone spatula as you go. This will take about 2 minutes in a high-powered blender like a Vitamix, or about 4 minutes in a food processor.
Taste and adjust for seasonings, adding more miso paste for a rich umami bite, more lemon juice for acidity, or more mustard for sharp pungency.