Arrange a rack in the top third of the oven and another on the lowest level. Heat oven to 425 degrees.
Slice 3 of the garlic cloves thinly but not paper thin; set aside the other 2 for the tahini yogurt.
Transfer the beans to a clean dish towel. Gently rub to remove as much moisture as you can without crushing them. On a rimmed sheet pan, gently toss the beans with 2 tablespoons olive oil, 1 tablespoon oregano, 1 teaspoon salt and a generous amount of coarsely ground black pepper. Taste a bean and add more salt if needed for the beans to taste well-seasoned. Spread in a single layer.
In a 13-by-9-inch baking pan, combine the tomatoes, sugar (use only ½ teaspoon if the tomatoes are very sweet), the sliced garlic and remaining ½ teaspoon oregano. Drizzle with 1 ½ tablespoons olive oil, a heaping ½ teaspoon salt and a generous amount of coarsely ground black pepper. Toss well with your hands.
Roast the tomatoes on the top rack and the beans on the bottom for 25 minutes. If the tomatoes are wrinkly and starting to burst, they’re done. (Larger tomatoes may need another 5 minutes.) If the beans are golden, crispy and split open, they’re done. If not, shake the pan back and forth and roast for 5 minutes more.
While everything roasts, make the tahini yogurt: Into a bowl, finely grate the zest from the lemon, then halve the lemon and squeeze in 2 tablespoons juice. Grate the remaining 2 garlic cloves into the same bowl. Add the yogurt, tahini, coriander, Aleppo pepper, ½ teaspoon salt and coarsely ground black pepper to taste. Stir to combine, then taste and add more salt, lemon juice for brightness, or more tahini for nutty richness. Cover and refrigerate until ready to use, up to 3 days.
When ready to serve, smear the tahini yogurt across a serving platter. Spoon the roasted tomatoes on top (keeping the juices for the arugula) and scatter the beans on top. Pile the arugula on top and drizzle with the tomato juices from the pan. Squeeze on a bit of lemon, add a pinch of salt or pepper (or both), and toss the arugula with your hands. Scoop up everything with bread.
