This dish is full of zesty lemon, minty tarragon, and fresh asparagus, making it a great weeknight spring dinner.
In a large saucepan, melt the butter over medium-high heat. When it foams, add the pasta and cook, stirring occasionally, until browned, 3 to 4 minutes. Add the rice and stir until coated, about 1 minute; season with salt and pepper. Add the stock. Bring to a boil. Cover and reduce heat to low. Cook until the rice is almost tender, about 10 minutes. Stir in the asparagus. Cover and cook until the rice and asparagus are tender, 4 to 5 minutes more. Remove from heat. Add the lemon zest and juice. Fluff the rice with a fork.
Meanwhile, season the chicken with salt and pepper. In a large skillet, heat the oil, two turns of the pan, over medium-high. Add the chicken and cook, turning occasionally, until golden and cooked through, about 8 minutes. Transfer to a plate and cover with foil to keep warm.
Add the butter to the skillet. When it foams, add the shallots and garlic. Cook, stirring often, until the shallots soften, about 2 minutes. Add the wine; cook, swirling the pan often, until slightly reduced, about 5 minutes. Add the stock. Reduce heat to a simmer. Stir in the crème fraîche, tarragon, lemon zest and juice, and Dijon; season. Add the chicken and spoon some of the sauce on top. Simmer at a very low bubble until the chicken is warm.
Divide the rice among plates or shallow bowls. Using tongs, transfer the chicken to a cutting board. Using a sharp knife, slice each chicken breast on an angle and fan on top of the rice. Spoon the remaining sauce on top.