For the beef: Drizzle the tenderloin all over with olive oil. In a bowl, combine the paprika and salt. Place plenty of black pepper on a plate. Sprinkle the paprika and salt mixture on the beef, then press the beef into the pepper to coat. Wrap tightly and rest at room temperature for 2 hours.
Preheat the oven to 450 degrees F. Unwrap the beef and place on a wire rack set on a baking sheet. Roast until the internal temperature is about 120 degrees F, 25 to 35 minutes. Remove and rest at room temperature or refrigerate.
For the pesto: In a food processor, combine the parsley, pecans, rosemary, sage, mint, garlic and lemon zest and juice. Pulse while slowly adding enough olive oil until the desired consistency is reached, like a dip. Taste and season with salt. Refrigerate until needed.
To serve: Slice the beef and serve warm or at room temperature alongside the pesto, crackers and crostini.