Preheat your oven broiler to high and place the rack in the upper third of the oven.
In a large bowl, toss the shredded chicken and sliced mushrooms with the Thai sweet chili sauce and half of the oil until evenly coated.
Spread the chicken and mushroom mixture onto a baking sheet in a single layer. Broil for 5-8 minutes, watching closely, until the sauce caramelizes and the mushrooms are tender.
While the chicken broils, combine sliced cucumbers, radishes, chili garlic sauce, rice vinegar, and remaining oil in a medium bowl. Toss to coat.
Divide the cooked jasmine rice into bowls.
Top the rice with the caramelized chicken and mushroom mixture.
Add a generous scoop of the cucumber and radish salad to the side of the bowl.
Garnish with fresh cilantro and serve immediately.