1. Heat oil in a large skillet over medium heat until hot. Add onion, carrots, and potatoes; cook, stirring occasionally, until they start to soften, 6 to 8 minutes. If vegetables begin to stick, add a little slosh of chicken broth to skillet.
2. Add garlic and curry powder; cook, stirring until fragrant, about 2 minutes. Add rice, broth, and pepper. Bring to a boil. Reduce heat to medium-low, cover, and simmer for 15 minutes.
3. Add shrimp; stir, cover, and cook, stirring occasionally, until shrimp are opaque and rice is tender, another 5 to 7 minutes. Sprinkle with basil and serve.
Note: Over and over in the recipes in this book I use the phrase "in a heavy skillet." Nonstick skillets have their place, but if I could have only one pan in my entire kitchen, I would choose a big cast-iron skillet. They're amazingly versatile and cook evenly. Once you get one seasoned (smear it with Crisco, then bake for an hour at 350°F), they're almost as easy to clean as nonstick. And they last forever – literally – whereas every nonstick pan I have ever owned eventually left me wondering how much Teflon my kids were ingesting along with their fried rice.