In a small saucepan over medium, combine the orange zest and juice, 214 grams (1 cup) sugar and ½ cup water. Bring to a simmer over medium and cook, stirring once or twice, until the sugar has dissolved and the syrup thickens, 3 to 5 minutes; you should have about 1 cup. Transfer the orange zest to a cutting board and finely chop; set aside. Stir the rum into the syrup. Cool to room temperature, then cover and set aside.

In a liquid measuring cup or small bowl, whisk together the whole eggs, yolks and ¼ cup water. In a stand mixer with the dough hook, mix the flour, yeast, remaining 40 grams (3 tablespoons) sugar and salt on low until combined. With the mixer running, slowly add the egg mixture. Knead on medium until a wet, slightly lumpy dough forms, about 2 minutes, scraping the bowl once or twice.

Add the 57 grams (4 tablespoons) butter and knead on medium, scraping the bowl once or twice, until the dough is smooth, elastic and forms a mass around the hook that mostly pulls away from the sides of the bowl, 7 to 9 minutes. Detach the bowl and hook, then lift out the hook with dough clinging to it; the dough should fall in a thick, shiny, sticky rope; if it does not, knead for a couple more minutes and retest. Add the chopped orange zest and mix on medium to combine, about 1 minute. Scrape the sides of the bowl and gather the dough in the center. Cover tightly with plastic wrap and let rise at room temperature until doubled, 1 to 1½ hours.

Meanwhile, using a pastry brush, liberally coat the insides of the 8 outer cups of a standard 12-cup muffin pan with the remaining 28 grams (2 tablespoons) butter, leaving the cups in the center row empty.

When the dough has doubled, use lightly oiled hands and a large spoon to scoop dough into the prepared cups until each is about two-thirds full; the dough will be stretchy and sticky, so you may need to “cut” the dough with the edge of the spoon. Mist a large sheet of plastic wrap with cooking spray, then lay it over the pan, greased side down. Let rise at room temperature until doubled, 30 to 40 minutes. Meanwhile, heat the oven to 350°F with the rack in the middle position.

Uncover the pan and bake until the babas are golden brown and a toothpick inserted at the centers comes out clean, 16 to 18 minutes. Meanwhile, in a stand mixer with the whisk attachment, beat the cream and 2 tablespoons rum syrup on medium-high until the mixture holds soft peaks, 2 to 3 minutes. Cover and refrigerate until ready to use.

When the babas are done, cool in the pan for 5 minutes. Gently lift each out and set on a wire rack. Cool for another 5 minutes, then brush the outsides of the warm babas with about ½ cup rum syrup. The babas can be served right away or kept on the rack at room temperature for up to 2 hours.

To serve, halve each baba lengthwise and place 2 halves, cut sides up, on each serving plate. Drizzle the cut side of each half with about 1 tablespoon of the remaining rum syrup. If needed, re-whisk the whipped cream to soft peaks, then dollop onto the babas. Serve right away.