Whisk the tamari, fish sauce, coconut sugar, and lime juice in a small bowl until the sugar is fully dissolved.
Mince the garlic, shallot, and bird's eye chili together into a fine paste using a knife or mortar and pestle.
Heat the avocado oil in a large non-stick skillet over medium-high heat until it begins to shimmer.
Add the garlic-chili paste to the hot oil and sauté for 30 seconds until the aroma becomes vibrant and fragrant.
Add the ground chicken breast to the skillet, breaking it into small crumbles, and cook until browned and no longer pink.
Toss in the sliced red bell pepper and trimmed green beans, stir-frying for 3-4 minutes until the vegetables are tender-crisp.
Pour the prepared sauce over the chicken and vegetables, tossing constantly to glaze every piece evenly.
Remove the pan from the heat and stir in the fresh Thai basil leaves until they are just wilted.
Portion the warm quinoa into a bowl, top with the lean basil chicken mixture, and season with sea salt and black pepper.