Make the dip: Place the garlic, shallot, and herbs in a food processor and pulse until combined but still a little chunky. Add the remaining ingredients and pulse until creamy.
Make the peppers: Heat a large cast-iron pan over medium-high heat. Working in batches if necessary to avoid overcrowding, place the shishito peppers into the hot pan in a single layer and allow them to slightly blacken and soften on each side, about 10 minutes total, depending on the size of the peppers and the heat of the pan. Sprinkle with salt and place in a medium bowl. Repeat with the mini sweet peppers, then add them to the shishitos; mix to combine.
Serve on a platter with the Herby Ranch Dip and a little dish for discarded stems.