Pat tilapia dry with paper towels. Combine coriander, pepper, and ¾ teaspoon of the salt in a small bowl. Season tilapia all over with the mixture.
Heat 1 tablespoon of the oil in a large skillet over medium-high. Add tilapia and cook until golden brown and crispy, about 4 minutes. Flip and cook until just opaque, about 1 minute. Transfer to a plate and cover to keep warm.
Add remaining 1 tablespoon oil to skillet. Add carrots and cook, stirring often, until almost tender, about 3 minutes. Add leeks and cook, stirring often, until tender, about 3 minutes. Add wine and lemon juice. Bring to a boil and cook until liquid is reduced by half, about 1 minute. Add rice, broth, and remaining ¼ teaspoon salt. Bring to a boil and cook, stirring often, until most of the liquid is absorbed, about 3 minutes. Add spinach and cook, stirring constantly, until wilted, about 1 minute.
Serve tilapia with brown rice, vegetables, and lemon wedges.
