Start by preheating your oven to 350 degrees F and greasing your 9x13-inch baking dish thoroughly. Bring a large saucepan of lightly salted water to a rolling boil over medium-high heat. Add the chicken breasts and cook for 7-10 minutes until they reach an internal temperature of 165°F and juices run clear when pierced with a knife.
Remove the cooked chicken to a cutting board and let it cool completely before handling. In your large mixing bowl, beat the softened cream cheese until smooth and fluffy using an electric mixer. Add crushed garlic, cumin, salt, and pepper, beating until well incorporated and the mixture is creamy without lumps.
Fold in the drained diced tomatoes, chopped green onions, diced green chiles, fresh cilantro, and lime juice into the cream cheese base. Add 1 cup of the shredded cheddar cheese and mix gently to distribute evenly. Shred the cooled chicken using two forks and fold it into the cream cheese mixture until every piece is coated.
Place about ½ cup of the chicken mixture in the center of each flour tortilla, being careful not to overfill. Roll the tortilla tightly around the filling and place seam-side down in your prepared baking dish. Arrange all enchiladas snugly in the dish, then top with the remaining cheddar cheese and pour the green enchilada sauce evenly over everything.
Bake the assembled enchiladas in your preheated oven for 20 minutes until the cheese is melted and bubbly. The enchiladas should be heated through and the sauce should be simmering around the edges. Let them rest for 5 minutes before serving to allow the filling to set slightly and prevent spillage when cutting.