In a small skillet or saucepan, combine the oil and rosemary sprigs. Bring to a simmer over medium heat until the rosemary begins to sizzle, then turn the heat to its lowest setting and cook for 5 minutes. Set aside to cool for 20 minutes, then discard the rosemary sprigs and pour the oil into a large bowl.

Meanwhile, position a rack in the center of the oven and preheat the oven to 350°F. Spray a 9-inch round cake pan at least 2 inches deep with cooking spray, and line the bottom with parchment paper, then flour the sides.

Add the sugar to the bowl with the rosemary oil and whisk until combined. Add the eggs and whisk vigorously until thick and glossy. Add the vanilla, sour cream, lemon zest, and lemon juice and whisk until smooth.

In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Pour the dry ingredients into the wet ingredients and whisk gently until only small lumps remain. Pour the batter into the prepared pan.

Bake until the edges of the cake are golden brown and a toothpick comes out clean, 55 minutes to 1 hour. Let cool for 30 minutes in the pan before inverting onto a wire rack to cool completely.