Bring a large pot of heavily salted water to a boil over medium heat. Stir in the orzo and cook as the label directs. Drain in a colander and rinse under cold water until cool. Drain, shake off the excess water and transfer to a large bowl.
Meanwhile, heat 2 tablespoons garlic olive oil in a large skillet over medium-high heat. Add the squash, season with salt and pepper and cook, stirring occasionally, until it begins to brown, about 4 minutes. Remove from the heat and cool to room temperature.
Add the squash to the bowl with the orzo. Stir in three-quarters of the feta, the mint, the remaining 2 tablespoons garlic olive oil, and salt and pepper to taste. Top with the remaining feta and more mint.