Heat 1 Tbsp. oil in a large skillet over high heat. Add garlic and 1 chile and cook, stirring, until fragrant, about 30 seconds. Add beef, season with salt and pepper, and cook, breaking up with a spoon and pressing down firmly to help brown, until cooked through and nicely crisped in spots, 8–10 minutes. Add broth and 2 cups basil and cook, stirring, until basil is wilted, about 2 minutes.
Toss carrots, scallions, 1 Tbsp. lime juice, and remaining chile, 1 cup basil leaves, and 1 Tbsp. oil in a small bowl.
Mix soy sauce, fish sauce, sugar, and remaining 3 Tbsp. lime juice in another small bowl until sugar dissolves.
Top rice with beef and slaw and drizzle with soy dressing. Serve lime wedges alongside for squeezing over.
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