Lightly grease a 9-by-13-inch baking dish. Line 2 baking sheets with foil.
Cook the spaghetti according to the package instructions in a large pot of boiling salted water. Drain, rinse, and transfer the spaghetti to the baking dish.
Cut the chicken breast in to 3/4 – 1″ cubes, place on baking sheet. Season with Salt & Fresh Ground Black Pepper
Meanwhile, turn on the broiler and place a rack 6 inches away from the heating element. Place the grape tomatoes, jalapenos,garlic cloves and onion on one of the prepared baking sheet, skin side up. Place the 2nd sheet pan with the chicken on the second oven rack. Broil the vegetables, for 5 to 7 minutes, until the tomatoes, jalapenos, garlic, and onion are softened and have begun to blacken. Continue to cook the chicken for an additional 5 to 7 minutes.Remove from the oven, and when cool enough to handle, dice the tomatoes, jalapenos, garlic, and onion.
Turn the oven temperature down to 350°
To make the sauce: In a saucepan, melt the butter over medium-low heat. Whisk in the flour until well combined and slightly browned, about 30 seconds. Slowly pour in the milk and cook, stirring, until the sauce thickens just a bit, 3 to 5 minutes. (You want it to coat the back of your spoon). If it gets too thick, you can slowly add more milk, about a teaspoon at a time.) Once the sauce thickens, immediately turn off the heat and slowly stir in half of the cheeses, about 1/4 cup at a time, until melted and incorporated into the sauce. Stir in the diced vegetables, along with the cumin, cayenne, cilantro, and lime juice. Taste and adjust the seasonings, adding salt and black pepper to taste. Pour the sauce into the cooked spaghetti and then stir in the cooked chicken. Cover the spaghetti with the remaining cheeses.
Bake, uncovered, for 20 minutes, or until brown and bubbling. Garnish with cilantro before serving.