Adjust oven rack to middle position and preheat to 350F/180C. Grease a 10-inch pie dish, or a 9-inch springform pan. Set aside.
In a medium bowl, sift together flour, baking powder, and salt. Set aside. In a small bowl, toss together 3/4 cup (150g) sugar and lemon zest until combined.
In a standing mixer fitted with the paddle attachment, beat together butter and lemon-sugar mixture on medium speed until light and fluffy, about 3 minutes. Occasionally scrape down the sides and bottom of the bowl. Add the egg and beat until combined. Beat in vanilla extract. Add half of the flour mixture and beat on low speed just until combined. Beat in heavy cream just until combined, followed by the rest of the flour mixture. Do not over mix. Scrape batter into prepared pan and smooth the top.
In another small bowl, toss strawberries with lemon juice and 2 tablespoons sugar, then arrange them cut-side down on top of the batter, being careful not to press them in.
Bake for 10 minutes, then reduce oven temperature to 325F/160C and continue baking for 45-60 minutes, or until cake is golden brown, firm to the touch, and a skewer inserted into the center of the cake (and not into a juicy strawberry) comes out clean. If the top is browning too fast while baking, cover pan loosely with aluminum foil. Allow cake to cool completely on a wire rack.