Preheat the oven to 350°F (175°C). Line a 9x13-inch baking pan with parchment paper, leaving some overhang for easy removal.
In a large mixing bowl, beat ¾ cup softened butter with the granulated sugar until pale, smooth, and fluffy.
Add 1 egg and the vanilla. Beat until thoroughly incorporated.
In a separate bowl, whisk together the sifted flour, baking powder, and salt.
Gradually add the dry ingredients to the butter mixture, alternating with the whole milk. Mix just until a thick, smooth batter forms.
Spread approximately half of the cake batter evenly across the bottom of the prepared pan.
In a clean bowl, beat the softened cream cheese until completely smooth. Add the remaining egg and ¼ cup brown sugar, then beat until creamy.
Carefully spread the cream cheese mixture over the cake base.
In a small bowl, combine the remaining ¾ cup brown sugar, ¼ cup softened butter, and ground cinnamon until a thick cinnamon mixture forms.
Drop spoonfuls of the remaining cake batter over the cream cheese layer.
Distribute small spoonfuls of the cinnamon mixture over the batter. Use a butter knife or skewer to gently swirl the cinnamon mixture through the upper layer without completely blending the layers together.
Bake the Best Cinnamon Roll Bliss Bars for 25–30 minutes, or until the edges are lightly golden and the center appears set. A tester inserted into a cake portion should come out without raw batter.
Place the pan on a wire rack and allow the bars to cool completely.
To prepare the glaze, whisk together the powdered sugar, heavy cream, and vanilla until smooth. Add a little additional cream if you prefer a thinner consistency.
Spread or drizzle the vanilla glaze generously over the completely cooled bars.
Allow the glaze to set briefly, then lift the dessert from the pan using the parchment paper.
Cut into squares or rectangles with a sharp knife and serve.