Heat 2 teaspoons olive oil in a skillet over medium heat; cook and stir Swiss chard and garlic in hot oil until chard leaves have wilted, 3 to 5 minutes. Remove from heat and allow to cool.

Process basil, pecans, sea salt, Parmesan cheese, and remaining olive oil in a food processor until all the ingredients are well integrated. Add Swiss chard mixture and lemon juice to the food processor; continue pulsing until the mixture is puréed. Season with salt and pepper.