Combine egg yolks, cream, lemon juice, and lemon zest in a bowl; whisk thoroughly.
Melt butter in a saucepan over medium-high heat. Add rice; cook, stirring constantly, until opaque, 3 to 4 minutes. Add chicken broth; stir quickly. Bring to a boil. Reduce heat to low. Cover and simmer until rice is tender and liquid has been absorbed, 20 to 25 minutes.
Fold lemon-cream mixture into the rice; mix well. Stir in Parmesan cheese and parsley.