In a medium-sized bowl whisk the flour, 2 teaspoons of the cardamom, and salt.
In a small bowl whisk 2 of the eggs.
In a small saucepan over medium-low heat, combine the milk and granulated sugar, then add the butter. Whisk until the butter is melted, then remove the pan from the heat and let it cool to around 100 to 110 degrees (cooling below 120 degrees will prevent the yeast from dying). Whisk in the yeast and let the mixture sit for 10 minutes until the top foams and starts to bubble.
Pour the yeast mixture into a stand mixer with a dough hook. Add the whisked eggs and mix on low to combine.
Add the flour mixture, 1/2 cup at a time, and combine on low 1 to 2 minutes until all the flour is incorporated. Scrape down the sides of the bowl with a rubber spatula as needed.
Once the dough forms a cohesive ball, increase the mixer speed to medium and knead 10 to 12 more minutes, until the dough is glossy and smooth, not sticky. Alternatively, you can hand-knead the dough. Lightly butter a large mixing bowl and transfer the dough to it. Cover the bowl with a clean, damp kitchen towel or plastic wrap and set it in a warm spot for about 1 hour, or until the dough almost doubles in size. (If your house is cold, trying setting the bowl in front of the woodstove or in a beam of sunshine streaming through a window.)
Punch the dough down, replace the towel or plastic wrap, and let the dough continue rising for 30 minutes.
Preheat the oven to 375 degrees and line a rimmed baking sheet with parchment paper.
Punch the dough down again, then using a bench scraper, divide it into 3 equal balls and let the dough rest for 10 minutes on a floured surface. Then stretch each ball into a 15-inch rope. Lay the ropes side by side and braid them together, pinching each end to secure the braid. Place the loaf on the prepared baking sheet, tuck the ends of the loaf under, then let the dough rise for another 30 minutes.
Once the dough has finished rising, whisk the remaining egg with the heavy cream and remaining 1/2 teaspoon of cardamom. Generously brush the loaf with the mixture, making sure to get it into all the nooks and crannies. Sprinkle with the pearl sugar (or sliced almonds) and bake on the center oven rack for 25 to 30 minutes until the crust is golden brown. Cool the loaf on a wire rack, then slice and serve.
Leftovers can be wrapped tightly and stored on the counter for a day or so. Reheat by wrapping the loaf in aluminum foil and setting it in a warm oven for several minutes.