Preheat oven to 350°F (175°C). Line two 12-cup muffin pans with paper liners.
In a medium bowl sift (or whisk) together 1 ¾ cups flour, ¾ cup cocoa powder, ¾ teaspoon baking soda, and ¾ teaspoon salt. Set the dry mixture aside.
In the bowl of a mixer (or using a hand mixer), beat 1 ¾ cups sugar and ¾ cup (1 ½ sticks) butter, at room temperature, on medium speed until light and fluffy, about 2 minutes.
Add the 2 eggs one at a time, beating well after each addition. Add 1 teaspoon vanilla and mix to incorporate.
Add half of the dry ingredients to the butter mixture and beat on low just until combined.
Add 1 cup hot water and mix on low just until incorporated.
Add the remaining dry ingredients and beat on low just until blended. Do not overmix.
Let the batter rest 5 minutes. Stir in 1 ¼ cups bittersweet chocolate chips.
Divide the batter evenly among the lined muffin cups (about two-thirds full each). Bake for 22–25 minutes, or until a toothpick inserted into the center comes out with just a few moist crumbs.
Cool the cupcakes in the pans for 5–10 minutes, then transfer them to a wire rack and cool completely before filling.
To make the ganache filling and frosting: place the remaining 1 ¼ cups bittersweet chocolate chips in a heatproof bowl. Heat the 1 cup hot water until just boiling (microwave or stovetop), pour the hot water over the chocolate chips, and let stand for 1 minute. Whisk until smooth.
Let the ganache cool at room temperature until thick and spreadable, at least 2 hours. If it is still too thin after cooling, chill briefly and stir occasionally until it reaches a spreadable consistency.
Using your thumb, a cupcake corer, or a small spoon, press or remove a deep opening in the center of each cooled cupcake.
Spoon ganache into each opening, reserving some ganache for frosting.
Frost the cupcakes with the remaining ganache once it is thick enough to mound—use a spoon or small spatula to create generous peaks.
Cupcakes may be made a day ahead and stored at room temperature.