Halve and peel onion. Slice halves into thin strips. Hold romaine head at root end and chop coarsely. Core tomato and cut into 1/2" dice. Coarsely chop smoked almonds. Pat chicken breasts dry, and season both sides with 1/4 tsp. salt and a pinch of pepper.

Heat 2 tsp. olive oil in a medium non-stick pan over medium-high heat. Place chicken in hot pan and cook undisturbed until golden brown, 2-3 minutes. Transfer chicken to prepared baking sheet, seared side up. Reserve pan; no need to wipe clean. Roast until chicken reaches a minimum internal temperature of 165 degrees, 7-9 minutes. Transfer chicken to a medium mixing bowl and cover with plastic wrap. Cool at least 5 minutes. While chicken roasts, caramelize onions.

Return pan used to sear chicken to medium heat and add 1 tsp. olive oil. Add onions to hot pan and cook, stirring occasionally, until browned, 10-12 minutes. If pan becomes too dry, add water 1 Tbsp. at a time. Remove from burner and set aside.

Once chicken has cooled, shred into bite-sized pieces. Season with a pinch of salt and pepper.

Halve avocado and remove pit by carefully tapping pit with the blade of your knife so it sticks. Gently twist knife to release pit. Scoop out the flesh with a spoon. Cut avocado flesh into 1/2" dice. Place 1/4 the avocado (reserve remaining for salad) into a large mixing bowl and mash until smooth. Mix in rice vinegar, 2 Tbsp. water, and a pinch of salt and pepper.

Place romaine, chicken, caramelized onions, tomatoes, almonds, blue cheese, and remaining avocado in bowl with dressing and toss. Place a serving of salad on a plate or in a bowl.