Combine the lukewarm water and yeast in a small bowl, stirring gently to combine, and let it sit for 5 minutes until foamy—this activates the yeast and ensures it's alive and ready to work. Meanwhile, in a large mixing bowl, combine the flour, 1/4 cup sugar, salt, and ground cardamom, whisking together to distribute the seasonings evenly. Add the softened butter and the yeast mixture to the dry ingredients, then mix on low speed for 3-4 minutes until a shaggy dough forms. The dough should come together but won't be perfectly smooth yet—this is correct.
Transfer the dough from Step 1 to a lightly oiled bowl, cover with plastic wrap or a damp towel, and let it rise at room temperature for 1.5 to 2 hours until it increases in volume by about 50%—you're not looking for a dramatic doubling, just gentle rise. Once the rise is complete, gently press the gas out of the dough with your hand (don't knead it), then shape it into a 10x12 inch rectangle on a lightly floured surface. Wrap the rectangle in plastic wrap and refrigerate for at least 2 hours, or up to overnight. I like to chill overnight when I have time because it makes the dough easier to work with and improves flavor development.
While the dough chills, prepare your lamination butter by combining the 1.75 cups of cold, high-fat butter (Kerrygold works beautifully here) with the 1.25 tbsp flour in a mixing bowl. Mix on low speed for 2-3 minutes until the mixture is smooth, pliable, and creamy—it should have the same consistency as the dough so it spreads evenly without tearing. The flour helps prevent the butter from leaking out during folding. Keep this butter mixture at cool room temperature (around 65°F-70°F) so it stays pliable but doesn't soften too much; if it gets too warm, refrigerate it briefly.
Remove the chilled dough rectangle from the refrigerator and place it on a lightly floured surface. Roll it out gently to a 12x20 inch rectangle, then spread the butter mixture from Step 3 evenly across the entire surface, leaving a thin margin around the edges. Fold the dough into thirds like a letter—fold one short end over the middle third, then fold the remaining third over the top. You've now completed your first turn. Wrap in plastic wrap and freeze for 6 minutes to set the butter layers.
Remove the dough from the freezer and place it on a floured surface with the open fold facing you. Roll gently to a 10x18 inch rectangle, then fold into thirds again (second turn), wrap in plastic, and freeze for 6 minutes. Repeat this process one final time: roll to an 8x16 inch rectangle, fold into thirds (third turn), wrap in plastic, and freeze for 6 minutes. These three folds create the hundreds of thin butter layers that make croissants flaky. I find that freezing for exactly 6 minutes between turns keeps the butter at the perfect temperature—not too soft to blur the layers, but not so cold that it cracks.
After the third fold is complete, place the dough back in the freezer for a final 6-minute chill. The dough is now ready to be shaped into croissants or stored. If you're not using it immediately, you can wrap it tightly and refrigerate it for up to 24 hours, or freeze it for up to 3 months—just thaw it overnight in the refrigerator before shaping.