In a stand mixer fitted with the paddle attachment, add the milk, eggs, flour, sugar, yeast, and salt. Mix on low speed until the dry ingredients are completely moistened, about 2 minutes. Increase speed to medium and mix, scraping down the sides of the bowl as needed, until a glossy dough forms and pulls away from the sides, 9–11 minutes. Once the dough comes together, scrape the dough off the paddle, add the butter, and mix on low speed for 1 minute. Increase speed to medium and continue mixing, scraping down the sides and bottom of the bowl as needed, until the butter is incorporated, and the dough is very silky, shiny, and completely homogenous, 5–6 minutes. Mix in the chorizo, Parmesan, and chives until completely incorporated, 2–3 minutes more.
Lightly grease two 9x5-inch loaf pans with cooking spray. Turn the dough out onto a lightly floured work surface. Using a bench scraper or large knife, divide the dough into 12 equal pieces, about 2 ounces each. Shape each piece into a tight ball, then let rest for 10 minutes. Shape each ball of dough into a 3-inch-long oval. Transfer 6 ovals, seam-side down, to one of the prepared pans (their sides will be touching). Repeat with the remaining ovals and pan. Loosely cover both pans with plastic wrap and set aside at room temperature until very gassy, puffed, and just slightly more than doubled in size, about 2½ hours.
Preheat the oven to 325°F, with a rack in the center. Brush the tops of the loaves with the cream, then immediately transfer to the oven. Bake until the loaves are evenly golden brown and cooked through, 25–30 minutes. Remove from the oven and let cool slightly, 2–3 minutes. Unmold the loaves and serve warm.