In a large saucepan over medium heat, heat oil. Add white and light green scallion parts and garlic and cook, stirring occasionally, until fragrant, about 3 minutes.
Add kale, spinach, and artichokes; season with salt and pepper. Cook, stirring, until greens are wilted, about 2 minutes. Using a slotted spoon, transfer greens mixture to a plate.
In same saucepan over medium heat, cook broth and cream cheese, stirring, until a light, creamy sauce forms. Add tortellini, then bring to a boil over high heat. Cover, reduce heat to medium, and cook, stirring occasionally, until tortellini is tender and warmed through, 3 to 5 minutes.
Reduce heat to low. Return greens mixture to saucepan and cook, gently stirring to combine, until warmed through, about 1 minute. Remove from heat; season with salt and pepper.
Divide tortellini among bowls. Top with pine nuts, lemon zest, and reserved dark green scallion parts.
