Preheat oven to 350°.
Line a rimmed baking sheet with parchment paper. Set aside.
In a large bowl, combine flour, sugar, baking powder, salt, and lemon zest, whisking well.
Using a pastry blender, cut butter into flour mixture until mixture resembles coarse crumbs. Add white chocolate morsels, stirring to combine. Set aside.
In a liquid-measuring cup, combine cream (reserving 1 tablespoon for brushing) and vanilla extract. Add to flour mixture, stirring to combine. (If dough seems dry, add more cream, 1 tablespoon at a time, until dough is uniformly moist.) Working gently, bring mixture together with hands until a dough forms.
Turn out onto a lightly floured surface. Knead lightly 4 to 5 times. Using a rolling pin, roll dough to a ½-inch thickness. Using a 2-inch round scalloped-edge cutter, cut rounds from dough. Place scones 2 inches apart on prepared baking sheet. Brush tops of scones with reserved 1 tablespoon cream.
Bake until edges are golden brown and a wooden pick inserted in the centers comes out clean, approximately 17 minutes.
Serve warm.