Preheat oven to 350°F. Line 3 baking sheets with parchment.
In the large bowl of a stand mixer fitted with the paddle attachment, beat eggs and granulated sugar on high speed until sugar is incorporated and mixture is slightly fluffy, about 3 minutes. Mix in oil, cream, lemon zest and juice, baking powder, vanilla, and salt on low speed until just combined, about 1 minute. Add flour and mix on medium speed until a soft, tacky dough forms, about 2 minutes.
Transfer dough to a work surface and divide into 3 portions. Cover 2 portions with plastic and set aside.
On a lightly floured surface, divide dough into 12 (2-tablespoon) portions (about the size of a golf ball). Roll each to an 8" rope. Wrap rope into a circle, then tuck one end through the center to create a knot. Arrange on a prepared sheet. Repeat with remaining dough, spacing 2" apart with 12 per sheet.
Bake cookies until lightly golden brown, 14 to 16 minutes. Transfer to a wire rack and let cool.