Slice the chicken fillet horizontally to expose a larger surface, or divide it into thick slices. Season both sides of the chicken with a pinch of smoked paprika powder and Celtic sea salt. Rinse the fresh green asparagus under running water and trim the bottom tough two centimeters from the stems.
Heat the ghee or coconut oil in a skillet over medium-high heat. Place the chicken fillet in the pan and cook for approximately ten to twelve minutes until golden brown and cooked through. Add the asparagus to the pan with the chicken for the last six to eight minutes to cook together. For nice grill marks, you can alternatively cook the asparagus in a separate hot grill pan.
Remove the chicken fillet from the pan as soon as it is cooked through. Coat the warm meat generously with the fresh green pesto. The heat from the chicken will release the pesto's aromatics optimally.
Arrange the warm asparagus neatly on the plates. Place the pesto-coated chicken fillet alongside and serve immediately.