Gather all ingredients before starting the recipe.
Season rack with kosher salt and ground black pepper on all sides for at least one hour before cooking and leave at room temperature.
Peel and slice 1 whole blood orange and set aside until ready to plate.
Heat a large skillet over medium high heat for 1-2 minutes, add 1 tablespoon of butter. When the butter is sizzling, add the venison.
Sear each side for 2-3 minutes.
Add the remaining 2 tablespoons of butter to the hot pan with the venison, and baste the venison for 5-6 minutes with the hot butter.
Remove venison to a cutting board and allow it to rest for 5-10 minutes.
Slice each rack in half, remove the loin from one bone and place the slices on a serving plate.
Drizzle port wine sauce on top and around the venison and garnish with orange slices and baby arugula.