Melt the butter with the cooking oil in a saucepan over medium heat.
Mix the rosemary, thyme, and flour into the butter mixture; cook and stir until smooth, bubbling, and turns a light tan color, 10 to 15 minutes.
Stir the heavy cream into the flour mixture a little at a time, allowing each addition to incorporate fully before adding more. Stir the nutmeg, cinnamon, brown sugar, salt, and pepper into the cream mixture; cook and stir until smooth.