Wash the berries and dry them or allow them to thoroughly air dry.
Preheat the oven to 350 degrees.
Cream together the butter and sugars. Add the oil, egg and vanilla and beat until well combined.
Stir the salt, baking soda, and cream of tartar into the flour. Add flour mixture to the wet ingredients and mix until combined.
Scoop dough using a standard #40 cookie dough scoop (almost two tablespoons of dough). Roll each dough ball in granulated sugar then place on a lined cookie sheet. Use the bottom of a small cup to press the dough down into a disc about 2.5 inches in diameter. Edges will crack a little.
Bake the cookies about 12 minutes until edges feel set but cookies are not browned. Remove from cookie sheet and cool completely before frosting.
Beat together the softened cream cheese, granulated sugar, and vanilla. Once combined continue to beat for a couple of minutes until mixture is very smooth and sugar has dissolved (it should not taste grainy).
Once cookies are cool, frost each cookie, then top with berries. Store covered in the fridge until ready to serve. These sugar cookie fruit tarts are best eaten within 24 hours.