Preheat grill pan. Peel tomatoes by plunging first into boiling water until skins split, and then into ice water to make them cool enough to handle. Remove skins with your hands and cut tomatoes into chunks. Season steaks with salt and pepper on both sides. Set aside.
In a food-processor bowl, combine the herbs, except chives and garlic. Pulse several times to finely chop. Add tomato chunks and vinegar, pulse to combine, then with motor running, gradually add olive oil until the mixture is combined and emulsified. Scrape mixture into a bowl, stir in chopped chives and salt to taste.
Grill steaks starting on high, to get a good char on both sides. Then reduce heat to medium and continue searing to desired doneness. Pour herb oil onto a rimmed serving platter and remove the hot steaks from the grill. Place directly onto the herb oil, moving around with tongs and then turning to coat with the oil. Garnish with additional fresh herbs and finishing salt, if desired. Serve immediately.