Step 1
Place ¾ cup (94 g) all-purpose flour in a shallow bowl. Working separately, evenly pound 4 small skinless, boneless rooster breasts (about 6 oz. every) between 2 sheets of plastic wrap with a rolling pin (quicker than a meat mallet) to about ¼” thick. Season throughout with kosher salt and freshly floor pepper, then dredge in flour, shaking off extra; switch to a big plate.
Step 2
Warmth 3 Tbsp. extra-virgin olive oil in a big skillet over medium-high. Working in 2 batches and including extra oil between batches if wanted, cook dinner rooster till golden brown beneath, about 4 minutes. Flip and cook dinner on different facet till rooster is almost cooked via, 1–2 minutes. Switch again to plate.
Step 3
Cut back warmth to medium; add remaining 2 Tbsp. extra-virgin olive oil. Add 6 garlic cloves, thinly sliced, and cook dinner, stirring, till barely softened, about 30 seconds. Pour in ½ cup dry white wine and simmer, stirring often and scraping up any browned bits, till virtually fully diminished, 1–2 minutes.
Step 4
Improve warmth to medium-high and add ⅔ cup low-sodium rooster broth or ⅔ cup water blended with ¾ tsp. rooster bouillon paste, 3 Tbsp. unsalted butter, and ½ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt. Prepare dinner, stirring usually, till butter is melted and mixed, about 2 minutes. Stir in 2 tsp. soy sauce and 5 Tbsp. yuzu juice. Return rooster to skillet; cook dinner, spooning sauce over, till rooster is cooked via and sauce is diminished barely, about 3 minutes. Season with extra salt and add extra yuzu juice if wanted. Add remaining 2 Tbsp. unsalted butter; cook dinner, swirling pan, till sauce is shiny. Take away from warmth; season with extra 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 rooster in skillet. Serve with country-style bread alongside for dipping into sauce.