In a medium bowl, whisk together the flour, baking powder, and salt. Set it aside.
In a large bowl, whip together the cream cheese and butter until smooth. Add in the brown sugar, egg, and vanilla, and mix until smooth again.
Slowly add the flour mixture into the cream cheese mixture and slowly mix until just combined. Scrape down sides if needed.
Line a cookie sheet with parchment paper and place a tablespoon-sized dollop of dough 1 inch apart from each other. Place in the fridge and chill for at least 2 hours or up to overnight. If chilling overnight, it is important to cover the dough with plastic wrap.
Preheat your oven to 350 degrees. Move the cookies 2 inches apart from each other on the parchment-lined cookie sheet if needed and bake for 12 to 14 minutes until they no longer look glossy on top and the bottom edges start to brown slightly.
Let cool for 2 minutes on the cookie sheet. Use the other end of a wooden spoon or other utensil and press down slightly into the cookie making a little dent in the center. Quickly place 4-6 chocolate chips in the center of each cookie and let it melt.
Using a butter knife, gently spread the chocolate to make a chocolate center and tops with toffee bits. Place on a wire rack to cool completely and enjoy!