Preheat oven to 350°F. Line an 8x8-inch baking pan with parchment paper leaving a 2-inch overhang along each side.
For the base, combine oats, flour, brown sugar and salt in a large bowl. Mix to blend evenly and press out any lumps of brown sugar. Melt butter in a small bowl and in the microwave or over the stovetop in a small saucepan and add it to the bowl with the oat mixture. Stir together until evenly combined. Reserve about ⅓ cup of the mixture for topping and press the rest evenly into the pan. Bake for 12-14 minutes until it feels set and dry to the touch. Transfer to a cooling rack. Reduce oven temperature to 325°F.
For the filling, combine cream cheese and sugar in a medium bowl and beat with an electric hand mixer on medium speed until smooth and glossy. Beat in egg and vanilla until well incorporated. Mix in yogurt. Pour it over the base, scatter cherries on top and crumble over the reserved oat base mixture.
Bake for 25-30 minutes until lightly golden and the filling is just set in the centre. Transfer pan to a wire rack and let cool completely. Refrigerate for at least 2 hours before dusting with icing sugar and slicing into squares.