Preheat the oven to 400 degrees F.
On a sheet pan lined with parchment paper, toss the tomatoes and chickpeas with 1 tablespoon oil, 1 teaspoon kosher salt and 1/2 teaspoon black pepper. Spread them out in a single layer with the tomatoes cut side up.
Roast until the tomatoes are wrinkled and have deepened in color and the chickpeas are golden brown and crisp, about 30-35 minutes.
For the vinaigrette, whisk the garlic, mustard, oregano, 1/2 teaspoon kosher salt and 1/4 teaspoon black pepper, vinegar, lemon juice and 1/4 cup oil in a small bowl.
In a large bowl, combine the tomatoes, chickpeas, cucumbers, olives, onions, feta and parsley.
Drizzle the vinaigrette into the salad. Gently toss to combine.