How do you prevent veggies from burning in dishes that take longer to cook?
In a simmered dish, there should be little risk of burning.  Brown your chicken first, then remove from pan.  Add veg. and use it to help release the fond.  When the veg. begins to color, add liquid. Stir and scrape. Use more liquid in your simmer; that is, as it reduces, add more so that the veg does not burn. Return the chicken to pan, and be sure enough liquid remains to avoid burning.