Peel and finely chop 1 small onion. Peel and thinly slice 6 garlic cloves. Rinse ⅔ cup white rice in a fine-mesh sieve until water runs clear.
Heat ¼ cup plus 2 Tbsp. olive oil in a large saucepan over medium. Add garlic and cook, swirling pan often, until golden brown, 3–5 minutes; the garlic will continue to cook and darken slightly after it’s off the heat, so take it out once it’s a bit golden. Transfer to a small heatproof bowl, leaving 1 Tbsp. garlic oil in pot. Stir 2 teaspoons crushed red pepper flakes into garlic oil in bowl; set aside.
Add the onion to the 1 Tbsp. of garlic oil that remains in the in saucepan and cook over medium heat, stirring occasionally, until onion is translucent and beginning to take on some color, about 5 minutes.
Pour in 8 cups stock and stir to combine. Stir in rice, 1 lb. skinless, boneless chicken thighs, and 1 tsp salt. Bring to a boil, then reduce heat to low and bring to a gentle simmer. Simmer, uncovered, until chicken is cooked through, about 20 minutes.
Transfer chicken to a plate and sShred meat with two forks. Continue to simmer soup while you’re prepping the rest of your ingredients (this will concentrate the flavor of the broth).
Add spinach and shredded chicken to pot. Continue to simmer, stirring occasionally, until spinach is bright green and chicken is warmed through, about 2 minutes.
Remove pot from heat. Squeeze in lemon juice (being careful not to let any seeds fall in), season with 2 teaspoons salt (or more to taste), and stir to combine.
Divide soup among bowls. Drizzle with reserved garlic-chile oil. Tear 3 sprigs dill over, then top with a few grinds of black pepper.