Cook jasmine rice in 3 cups of water according to package directions. Set aside.

Heat canola oil in a large stockpot over medium-high heat. Season chicken with salt and pepper. Sear chicken pieces until golden brown on both sides, about 3-4 minutes. Transfer chicken to a plate and set aside.

Reduce heat to medium. Add shallots and garlic to the pot and cook, stirring frequently, until softened and fragrant, about 2 minutes.

Stir in red curry paste and grated ginger until fragrant, about 1 minute.

Pour in coconut milk. Add fish sauce and sugar. Bring to a boil, then reduce heat and simmer uncovered, stirring occasionally, until the sauce has thickened, about 10-15 minutes.

Stir in broccolini and cook until tender, about 3 minutes.

Remove from heat. Stir in green onions, cilantro, and lime juice. Season with salt and pepper to taste.

Serve immediately over the prepared jasmine rice.