Heat oil in a medium saucepan over medium-high heat until hot and shimmering but not smoking, about 2 minutes; add onion and cook, stirring occasionally, until softened and beginning to brown, about 5 minutes.
Add garlic, chili powder, coriander, cumin, salt, and sugar; cook, stirring constantly, until fragrant, about 30 seconds. Add chicken and cook, stirring constantly, until coated with spices, about 30 seconds.
Add tomato sauce and 3/4 cup water; stir to separate chicken pieces. Bring to simmer, then reduce heat to medium-low; simmer uncovered, stirring occasionally, until chicken is cooked through and flavors have melded, about 8 minutes.
Pour mixture through a medium-mesh strainer into a medium bowl, pressing on chicken and onions to extract as much sauce as possible; set sauce aside.
Transfer chicken mixture to a large plate; freeze for 10 minutes to cool, then combine with cilantro, jalapenos, and cheese in medium bowl and set aside.