Preheat the oven to 350°F (175°C). Position a rack in the lower third of the oven. Grease a bundt pan with some of the room-temperature butter and lightly dust it with cocoa powder or flour; tap out any excess. Set the pan aside.
In a medium bowl, sift together the 2 cups cake flour (or all-purpose flour), 1 1/3 cups Dutch cocoa powder (or regular), 2 teaspoons baking powder, 1 teaspoon baking soda, and 1 teaspoon salt. Set this dry mixture aside.
In the bowl of a stand mixer fitted with the paddle attachment (or in a large bowl with a hand mixer), beat the 1 cup (2 sticks) room-temperature unsalted butter, 1 cup granulated sugar, and 3/4 cup brown sugar on medium speed until the mixture is light and fluffy, about 3–4 minutes. Scrape down the bowl as needed.
Add the 3 large room-temperature eggs to the butter-sugar mixture one at a time, mixing briefly after each addition until just incorporated. Scrape the bowl.
In a separate bowl, whisk together the 1 cup room-temperature buttermilk, 1/2 cup vegetable oil, 1 cup full-fat Greek yogurt, 1 tablespoon espresso instant coffee powder, and 3 teaspoons vanilla extract until smooth. Set this wet mixture aside.
With the mixer on low speed, add the dry ingredients to the butter-egg mixture in three additions, mixing briefly and scraping the bowl between additions. Do not overmix.
Still on low speed, add the wet mixture in three additions, mixing only until each addition is incorporated and the batter is uniform. Stop mixing as soon as there are no large streaks of flour or wet ingredients.
Gently fold in the 3/4 cup mini chocolate chips by hand with a spatula until evenly distributed.
Spoon the batter into the prepared bundt pan, smoothing the top. Tap the pan gently on the counter a few times to remove large air pockets and level the batter.
Bake on the lower rack for 45–60 minutes, checking at 45 minutes. The cake is done when a toothpick inserted into the center comes out clean or with just a few moist crumbs. If the top is browning too quickly, tent loosely with foil.
Remove the cake from the oven and place the pan on a wire rack. Let the cake cool in the pan for 15 minutes.
After 15 minutes, invert the bundt pan onto a cake plate or wire rack to remove the cake. Allow the cake to cool completely, about 1 hour, before glazing.
To make the glaze: place the 1 1/2 cups semi-sweet chocolate chips and 3/4 cup heavy whipping cream in a microwave-safe bowl. Microwave in 20-second bursts, stirring well between each burst, until most of the chocolate is melted. Stir until smooth. Add the 1 teaspoon vanilla extract and stir to combine.
Let the glaze cool at room temperature until it thickens slightly and will pour slowly (a few minutes). Stir occasionally.
Place the cooled bundt cake on a rimmed plate or tray. Pour the glaze over the top, allowing it to drip down the sides. Sprinkle additional mini chocolate chips on top as a garnish if desired.
Let the glaze set for a few minutes. Slice and serve the cake at room temperature.