Oven-cured tomatoes require only a few minutes of hands-on preparation but must dry out overnight in the oven.
Heat oven to 250 degrees. Cut tomatoes crosswise into thirds. Place cut side up on parchment-lined baking sheet. Brush with oil; season with salt, pepper, sugar, and marjoram.
Place in oven. For a gas oven with pilot light, turn off heat after 2 hours; leave overnight. For an electric oven, bake 2 hours, then turn to warm; leave overnight.