Cut the peppers in half lengthwise and remove the seeds. Add the peppers to a bowl and toss lightly with oil, salt, and pepper.
Spread the peppers on a baking sheet and roast for 15 minutes until slightly softened and caramelized. Let cool to room temperature.
Meanwhile, add the goat cheese and cream cheese to the bowl of a food processor. Process until smooth and spreadable, scraping the bowl down as necessary.
Gently blend in herbs, lemon zest. Season to taste with salt. Transfer the cheese mixture to a piping bag fitted with a piping tip.
When peppers are room temperature, pipe the cheese mixture into each pepper half. (Note 1) Arrange on a serving platter and garnish with chopped herbs.
Refrigerate leftovers for up to 2 days.
For ease filling the piping bag with the cheese mixture, place the piping bag (fitted with a tip) in a tall glass. Fold the top of the bag down over the edge of the glass. Spoon the cheese mixture into the bag. Unfold the bag and squeeze the mixture towards the bottom of the bag and pipe.