Bring a large pot of heavily salted water to a boil over medium heat. Stir in the orzo and cook for 8 minutes; pasta will be slightly undercooked. Reserve 1/2 cup of the cooking water, then drain the orzo in a colander in the sink.
Heat 2 tablespoons oil in a large skillet over medium-high heat. Add the squash, season with salt and pepper, to taste, and cook, stirring occasionally, until beginning to brown and soften, about 4 minutes. Reduce the heat to medium-low, and add the cooked orzo and cooking water. Bring to a simmer and stir in 3/4 of the feta; season with salt and pepper. Cook until the water is absorbed, about 2 minutes. Remove from the heat and stir in the remaining 2 tablespoons oil and mint.
Transfer to a serving platter and sprinkle the remaining feta over the top and garnish with additional chopped mint.