Place an 8x8 baking dish (or similar) filled with 1 inch of water on the lower shelf of the oven. This is technically optional; we tested with and without and found that the brownies with the water bath were more even across the top, whereas the ones without rose a bit on the edges.
Preheat the oven to 350°F and line a metal 9x13-inch cake pan with parchment paper and spray lightly with cooking spray. Make sure some of the parchment is over the edge of the pan for easy removal. This may require two sheets, one going in each direction of the pan - make sure the one that goes across the shorter distance is under the one that goes along the full length of the pan. It can be helpful to grease the pan, too, to help the parchment stick.
Melt 1 cup salted butter in a heavy-bottomed saucepan over low heat. Add in 2½ cups granulated sugar and stir until smooth and the butter and sugar have started to emulsify and no butter is separated on top of the sugar. Remove from heat, transfer to a large bowl, and let the mixture cool for 5 minutes, stirring often to release heat.
Add 2 tablespoons canola oil and 1 tablespoon vanilla extract to the butter and sugar and mix them in with a rubber spatula until thoroughly combined and there's no separation between the ingredients (no oil resting on top).
Mix in 5 large eggs one at a time, beating with the spatula or a fork after each one. Mix until fully incorporated.
Sift the ¾ cup + 2 tablespoons all-purpose flour ¾ cup + 1 tablespoon unsweetened cocoa powder, and ¾ teaspoon salt into the butter and sugar mixture, stirring gently and minimally, until almost all the dry streaks are gone.
Fold in the ½ cup semi-sweet mini chocolate chips until completely incorporated and no dry streaks remain.
In a medium bowl, beat together 16 ounces cream cheese, 1 large egg, and 1 teaspoon vanilla bean paste until fully incorporated.
Add ½ cup granulated sugar and mix until smooth.
Pour about ⅔ to ¾ of the brownie batter into the prepared and dollop with half of the cheesecake mixture. Dollop on the remaining brownie batter and then top with the remaining cheesecake batter.
Use a butter knife to run through the brownie and cheesecake mixture with the wide side to truly displace and pull the batters along to swirl.
If using, sprinkle ¾ cup semi-sweet chocolate chips over the top of the batter before baking.
Bake for 45 to 50 minutes on the middle rack, rotating halfway through.
Remove from the oven and allow the brownies to cool completely (about 2 to 3 hours) before removing the brownies from the pan and slicing them with a large sharp knife into squares. We like using these plastic knives because they yield clean slices! The brownies can be chilled for 1 hour after cooling at room temperature for 2 hours for sturdier slices.