Coat the chicken breasts in the ancho chile powder and marinate for 4-12 hours.
Preheat the oven to 375°F.
In a large pot, bring the water, milk, butter and salt to a boil. Reduce heat to low and whisk in the polenta. Cook, stirring regularly, for 20 minutes. Fold the cheese into the polenta and cook for 10 more minutes, until melted. Season with salt and pepper.
On a baking sheet, toss the roma tomatoes, jalapeños, and yellow onion with the canola oil. Roast for 10-15 minutes, until browned. Transfer to a blender, along with the remaining roasted salsa ingredients. Blend until smooth and season to taste.
Arrange the chicken on a baking sheet. Roast for 15-20 minutes, or until cooked through. Let the chicken rest for 5-10 minutes before slicing.
On a baking sheet, toss the broccolini with the oil, salt and pepper. Roast for 8-10 minutes, until crisp.
To serve, divide the chicken breast, polenta and broccolini between plates. Top with roasted salsa.