Start by preheating the oven to 350F. Then in a large bowl or a stand mixer, blend the softened cream cheese about 1 minute until it's smooth. Add in the room temperature eggs and blend together until there are no lumps.
Add the oil to the mixture and combine. Then add the cake mix and mix just until there are no streaks of flour in the batter. Be careful not to overmix.
Combine the brown sugar and ground cinnamon in a small bowl and set aside.
Place half the cake batter into a greased 9X13 pan, spreading it to make a bottom layer. Then sprinkle over the brown sugar mixture evenly distributing it over the entire surface. Top with the remaining cake batter. You may need to dollop the batter over and then use the back of a spoon or an off-set spatula to carefully spread it evenly.
Bake in the oven for 25-30 minutes. Cover the cake with foil at 15 minutes to prevent the top from browning too quickly. When done, a toothpick should come out mostly clean with no wet batter.
While the cake bakes, use a whisk to mix together the powdered sugar, milk, and vanilla extract in a medium bowl until a smooth and pourable glaze is made. Cover with plastic wrap and set aside.
Allow the cake to cool on the counter for about 10 minutes. Then use a fork or toothpick to poke holes repeatedly over the surface of the cake. While the cake is warm pour half of the icing over so that it melts down into the poked holes. Let the cake cool for 30 minutes or so before adding the remaining icing.
Allow the cake to cool fully before slicing and serving.