In a small bowl, dissolve the yeast and sugar in hand-hot water. Cover the bowl and let it rest for 10 minutes to activate the yeast. (Hand-hot water should be warm enough to put your hand in without discomfort.)
In a large mixing bowl, combine the flour, salt, olive oil, milk, and the activated yeast mixture. Knead the mixture until the dough is moist, elastic, and not sticky. Form it into a ball, lightly coat with olive oil to prevent drying, and let it rise for about 2 hours.
For the zaatar topping, mix the zaatar and olive oil in a bowl. Adjust the oil as needed to get a spreadable consistency.
Preheat your oven at 230°C. Roll out the dough into small circles and place them on a baking sheet. Spread 1–2 teaspoons of the zaatar mixture onto each dough circle.
Bake in the oven for 10-12 minutes or until the manakeesh are slightly golden. Remove from the oven and allow to cool.
Once cooled, top each mini manakeesh with a dollop of labneh and garnish with chopped cucumbers, tomatoes, and fresh mint.