Heat 2 teaspoons of the olive oil in a frypan over medium heat; cook and stir the silverbeet and garlic in the hot oil until the silverbeet leaves have wilted, 3 to 5 minutes. Remove from heat and allow to cool.
Process the basil, pecans, sea salt, Parmesan cheese and remaining olive oil in a food processor until all the ingredients are well integrated. Add the silverbeet mixture and the lemon juice to the food processor; continue chopping until the mixture is pureed. Season with salt and pepper.