Preheat the oven to 350°F, ensuring the rack is set in the middle position. Sift the flour into a bowl to remove lumps.
In a stand mixer bowl, combine sugar, butter, baking powder, salt, and vanilla extract. Mix on low speed until combined, then increase to medium and beat until light and fluffy (about 5 minutes).
Whisk together the egg and cream. Gradually add the egg mixture to the batter in 5–6 additions, allowing each to incorporate fully.
Reduce the mixer speed to low and sprinkle in the sifted flour. Mix until a stiff, smooth batter forms.
Transfer the batter to a piping bag fitted with a ½-inch plain tip.
Pipe 1-inch-wide discs, spaced evenly, onto the parchment-lined baking sheets. Each disc should be about ⅜-inch thick.
Bake for 20 minutes or until the wafers are golden brown at the edges. Allow to cool completely on the baking sheets.
Store in an airtight container at room temperature for up to 2 months.