Arrange the pita halves cut-side up on a broilerproof sheet pan. Drizzle with 2 tablespoons of the oil and broil until crisp, 2 to 3 minutes.
Top with the red peppers, artichokes, almonds, Cheddar, and oregano. Broil until the cheese has melted, 2 to 3 minutes.
Divide the green beans among bowls. Drizzle with the lemon juice and the remaining 1 tablespoon of oil. Season with 1/4 teaspoon salt and 1/8 teaspoon pepper. Serve with the pizzas.