Put the rice in a bowl and fill with cold water. Swish the rice with your fingers to release excess starch, then pour off the water. Repeat 2 or 3 more times until the water is less cloudy. Drain the rice and transfer to a heavy-duty 3-quart saucepan. Add 2-3/4 cups water, set over high heat, and bring to a boil. Cover, lower the heat to low, and cook until the rice is tender but intact, about 30 minutes. Remove from the heat and let stand, uncovered, until cooled to room temperature. (The rice can be made up to 2 hours ahead.)
Meanwhile, heat the oil in an 8-inch skillet over medium heat. Add the shallots and cook, stirring often, until translucent, 2 to 3 minutes. Stir in the chile, if using, and cook, stirring, for 1 minute. Remove from the heat.
Combine the lime juice, rice vinegar, fish sauce, and 1/2 tsp. salt in a large bowl.
Wet a large wooden spoon with water and use it to turn the rice gently to loosen it. Transfer to the bowl with the dressing, add the shallot mixture, and gently toss to combine. Let the salad sit at room temperature for at least 10 minutes and up to 1 hour to let the flavors blend. Stir in the sugar snap peas, diced avocado, and half of the mint; season to taste with salt. Transfer to a shallow serving dish and garnish with the sliced avocado and the remaining mint. Serve at room temperature with the lime wedges on the side.