Slice the yellow onion into thin half-moons and mince the garlic cloves.
Heat 0.5 tbsp of olive oil in a large skillet over low heat; add onions and a pinch of salt, cooking for 40 minutes while stirring occasionally until deeply browned and jammy.
While onions cook, dice the chicken breast into one-inch pieces and toss in a bowl with smoked paprika, dried thyme, half the sea salt, and half the black pepper.
Remove caramelized onions from the skillet and set aside; increase heat to medium-high and add another 0.5 tbsp of olive oil.
Add the chicken to the skillet, searing for 6 minutes until golden and cooked through, then remove and set aside with the onions.
Add the remaining 0.5 tbsp of olive oil to the skillet along with sliced mushrooms, diced zucchini, and sliced red bell pepper.
Sauté the vegetables for 8-10 minutes until tender and slightly charred, then stir in the minced garlic for 1 minute.
Return the chicken and caramelized onions to the skillet; pour in the balsamic vinegar and stir for 2 minutes to deglaze the pan and coat everything in a glossy glaze.
Season the entire skillet with the remaining sea salt and black pepper.
Serve the savory chicken and vegetable mixture over the warm cooked brown rice and top with the fresh sliced avocado.