Step 1
Place ¾ cup (94 g) all-purpose flour in a shallow bowl. Working one at a time, lightly pound 4 small skinless, boneless chicken breasts (about 6 oz. each) between 2 sheets of plastic wrap with a rolling pin (faster than a meat mallet) to about ¼” thick. Season all over with kosher salt and freshly ground pepper, then dredge in flour, shaking off excess; transfer to a large plate.
Step 2
Heat 3 Tbsp. extra-virgin olive oil in a large skillet over medium-high. Working in 2 batches and adding more oil between batches if needed, cook chicken until golden brown underneath, about 4 minutes. Turn and cook on other side until chicken is nearly cooked through, 1–2 minutes. Transfer back to plate.
Step 3
Reduce heat to medium; add remaining 2 Tbsp. extra-virgin olive oil. Add 6 garlic cloves, thinly sliced, and cook, stirring, until slightly softened, about 30 seconds. Pour in ½ cup dry white wine and simmer, stirring occasionally and scraping up any browned bits, until almost completely reduced, 1–2 minutes.
Step 4
Increase heat to medium-high and add ⅔ cup low-sodium chicken broth or ⅔ cup water mixed with ¾ tsp. chicken bouillon paste, 3 Tbsp. unsalted butter, and ½ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt. Cook, stirring often, until butter is melted and combined, about 2 minutes. Stir in 2 tsp. soy sauce and 5 Tbsp. yuzu juice. Return chicken to skillet; cook, spooning sauce over, until chicken is cooked through and sauce is reduced slightly, about 3 minutes. Season with more salt and add more yuzu juice if needed. Add remaining 2 Tbsp. unsalted butter; cook, swirling pan, until sauce is glossy. Remove from heat; season with more pepper.
Step 5
Toss 3 scallions, thinly sliced on a deep diagonal, a pinch of salt, and remaining 1 Tbsp. yuzu juice in a small bowl to coat.
Step 6
Scatter dressed scallions over chicken in skillet. Serve with country-style bread alongside for dipping into sauce.