Preheat the oven to 450°F (230°C) and place a rack on the lowest shelf. Generously grease a popover pan or a muffin pan.
Combine the eggs and milk in a blender and blend until smooth.
Add the flour to the blender and blend until the batter is smooth and free of lumps.
Transfer the batter to a bowl and stir in the grated Parmesan and the basil-walnut pesto until evenly combined.
Place the greased pan in the hot oven for 2 minutes to heat the pan.
Carefully remove the hot pan and pour the batter into each cup about half full.
Bake at 450°F (230°C) for 20 minutes without opening the oven door.
Reduce the oven temperature to 350°F (175°C) and continue baking for another 10–15 minutes, or until the popovers are lightly browned and puffed.
Remove from the oven and serve warm.