In a medium bowl, stir together the yogurt and salt.
Lay a linen towel or several layers of cheese cloth in a medium bowl. Add the yogurt mixture and gather the edges, twist or tie a knot. Place a seive over a deep bowl and add the towel with the yogurt into the seive, making sure it doesn't touch the bottom. Place in a cool place or the refrigerator for 24 hours to drain. I found this is long enough to enjoy it as a dip.
Heat a heavy skillet over high heat. When hot, add olive oil and tomatoes. Cook for 4-5 minutes, and once they burst and slightly charred, add garlic and sauté for about 1 minute, long enough for the aroma is released from the garlic. Season with salt and pepper.
Remove yogurt mixture from the refrigerator and give a stir. Spread it into a serving plate, making grooves with the back of the spoon, then drizzle the olive oil into the grooves. Lay the warm heirloom and vine cherry tomatoes over the labneh and add olives, capers, additional heirloom tomatoes, oregano and thyme. Drizzle some of the liquids from the skillet. Garnish with dill, oregano and parsley.
Serve with pita bread and sliced garlic baguettes.
