Set oven to 325 F and oil or butter a 13x9 baking pan. Peel and chop apples in a small dice and set aside. Optional: lightly toast chopped pecans if desired, and set aside.
In a mixing bowl large enough to hold all ingredients, stir together flour, soda, and salt.
In separate, smaller bowl, beat butter, oil and sugar until combined, then add eggs and continue beating until combined.
Stir in liqueur, vanilla, apples, and pecans until well combined.
Pour into prepared pan and bake 45 minutes.
Remove from oven and place on rack to cool.
While cake is baking, make the icing.
In a small pot, heat butter and sugar, uncovered, over medium-low heat. Stir to combine as butter and sugar melt.
Once butter and sugar mixture begins to simmer and sugar is melted, remove from heat and add liqueur, vanilla, and cream. Return to heat but do not boil, and cook just below a simmer for about 5 minutes.
Remove from heat and allow to cool about 15 minutes before placing uncovered in the refrigerator to chill about 30 minutes.
Pour icing into a cold bowl and beat about 3 minutes. Icing will turn a paler shade and thicken. Once beaten, ice the cake.
To serve, cut into small squares with a scoop of ice cream or sweetened whipped cream.
