Preheat oven to 350 degrees F.
In a large mixing bowl, cream butter, 1 cup of sugar and the powdered sugar. Add vegetable oil, lemon juice, lemon zest and eggs and mix well.
In a separate bowl, combine dry ingredients. Add to wet ingredients and mix until well incorporated.
Roll dough into 1 inch balls and place on cookie sheet.
On a large plate, spread ¼ c of sugar. Find a smooth bottomed glass, dampen with water and press it into the sugar to coat the bottom of the glass in sugar. Then press the sugar-coated glass into the cookie dough balls and lightly press down until your dough begins to flatten and the edges around the glass begin to split. Repeat wetting and dipping the glass into sugar for each cookie.
Bake at 350 degrees for 8 minutes. Cool cookies on a cooling rack and then put them in the fridge until you are ready to frost them.
Combine butter, powdered sugar, and sour cream in a medium mixing bowl and beat until smooth. Add jam and mix until just blended. Frost cookies when you are ready to serve.