In a 2- to 3-quart pan over high heat, bring 2 1/2 cups water and the salt to a boil. Gradually whisk in cornmeal and stir until mixture is thick and smooth, about 1 minute. Remove from heat.
In a bowl, beat eggs and buttermilk just to blend. Whisk into cornmeal mixture until completely incorporated. Stir in chilies and chili powder. Scrape mixture into a buttered 8-inch square baking dish.
Bake in a 400° regular or convection oven until top is browned and a wooden skewer inserted in the center comes out clean, about 35 minutes. Let stand 10 minutes. Scoop out portions with a spoon and serve with Avocado Salsa.