Bring a large pot of water to a boil. Cook fettuccine according to package directions. Drain, reserving 1 cup cooking water.
Meanwhile, whisk broth, cream cheese, garlic and salt together in a medium bowl until the cream cheese is in pea-sized chunks.
Heat oil in a large skillet over medium-high heat. Add Brussels sprouts, shallot and crushed red pepper; cook, stirring often, until the Brussels sprouts are bright green and slightly softened, 2 to 3 minutes. Add wine; cook, stirring often, until mostly evaporated, about 1 minute. Add the broth mixture, stirring constantly to melt the cream cheese; bring to a light simmer over medium-high heat. Reduce heat to medium; cook, stirring occasionally, until thickened, about 1 minute.
Stir in chicken, artichokes, the fettuccine and ½ cup of the reserved cooking water. Cook, tossing constantly and adding the remaining ½ cup cooking water, a splash at a time, until the fettuccine is coated in sauce, about 2 minutes. Remove from heat. Add lemon juice and ¼ cup basil; toss to incorporate. Top with the remaining 2 tablespoons basil.
