Prepare flour mixture: Sift the flour into a medium bowl and mix in 1 1/2 teaspoons of salt. Set aside.
Activate yeast mixture: In a large bowl, combine instant yeast and sugar. Pour in warm water (~112°F/44°C) and stir until sugar dissolves. Mix in vegetable oil.
Make dough: Add the flour mixture to the wet ingredients and mix with a spatula until just combined. Cover with a kitchen towel and let rest for 10 minutes.
Knead dough: Knead the dough by hand for about 5 minutes until smooth and cohesive. Form into a ball and place in a lightly oiled bowl. Cover with plastic wrap and a towel. Let rise in a warm place for about 1 hour or until doubled in size.
Divide dough: Divide the dough into 18 equal pieces, about 50-52 grams each. Shape each piece into a ball. Place on a tray, cover with plastic, and rest for 15 minutes.
Prepare zaatar topping: In a bowl, mix chopped tomatoes, chopped onions, 3/4 teaspoon salt, zaatar, and olive oil until well combined.
Shape dough and assemble: Roll each dough ball into a disk about 12 cm diameter using a rolling pin. Place on ungreased half-sheet pans (3 pans, 6 pieces each). Press the center gently with fingers to form a rim around the edges.
Add topping: Spread about 1 1/2 tablespoons of the zaatar mixture evenly on each dough disk, pressing lightly so it sticks.
Final rest: Cover the trays with plastic and let the assembled manakish rest for 15 to 30 minutes before baking.
Bake: Preheat oven to 425°F (220°C). Bake on the lower-middle rack for 8 to 10 minutes until golden brown and cooked through.
Serve: Remove from oven and serve immediately while hot.