In a large bowl, place butter at room temperature, powdered sugar, honey, lemon zest, lemon juice, and vanilla extract.
Using a hand mixer, or a stand-up one, mix the ingredients on low speed until the sugar is incorporated. Increase the speed to high and mix for 2-3 minutes.
Add the eggs and keep mixing on medium speed.
In a separate medium bowl, sift together flour, salt and baking powder.
Add the flour slowly to the batter and keep mixing on low speed until the batter is smooth.
Add the fruit and mix gently to incorporate them.
Prepare a baking pan by buttering the bottom of it. Cover the pan with parchment paper.
Pour the batter into the baking pan and level it with a spatula.
Bake at 350F/180C for 30-35 minutes or until the top of the cake is golden brown.
Let it cool, then serve cut in squares sprinkled with powdered sugar on top.