In a 12-inch skillet over medium-high, heat the oil and butter until the butter melts. Add the onion, tomatoes and 1 teaspoon salt, then cook, stirring occasionally, until the onion has softened and the tomatoes begin to release their juice, about 5 minutes.

Add the tomato paste and cook, stirring, until the tomato paste begins to brown, about 1 minute. Stir in the garlic and cook until fragrant, about 30 seconds.

Add the rice and cook, stirring constantly, until the grains are translucent at the edges, 1 to 2 minutes.

Remove the pan from the heat and stir in the ouzo. Return to medium-high and bring to a simmer, then cook, stirring, until most of the moisture has been absorbed, about 1 minute.

Stir in 3 cups of the hot water and 1½ teaspoons salt. Bring to a boil, then reduce to medium and cook uncovered, stirring often and briskly, until the rice is al dente (tender but with some firmness at the center) and the consistency is creamy but still rather loose, 8 to 10 minutes; adjust the heat as needed to maintain a vigorous simmer.

If the rice is thick and dry but the grains are still too firm, add the remaining ½ cup hot water and continue to cook, stirring, until the rice is al dente.

Off heat, stir in the oregano and lemon juice, then taste and season with salt and pepper. Transfer to a serving bowl and sprinkle with the feta. Serve with oil for drizzling.