In the bowl of a stand mixer fitted with a dough hook, add brown sugar, salt, 3.5 cups of flour, and yeast. Stir to combine. Add eggs and egg yolk, milk, butter, and lemon zest. Turn mixer to low until mixture is combined. Slowly add remaining (approximate) ½ cup of flour, a few tablespoons at a time, mixing on low speed until a dough is formed. It should be quite tacky and soft, but if it is too wet, add more flour until desired consistency. Increased speed to medium to medium high and mix for 5-6 minutes, until dough is smooth and elastic.
Remove dough from mixer and place in a lightly oiled bowl. Cover with plastic wrap and place in a warm, draft-free spot. Allow to rise until doubled in size, about 1 hour.
Punch dough down, and divide in half. Melt white chocolate chips over a double boiler or in a small microwave safe bowl, heating in 15-30 second intervals, stirring in between, until melted and smooth. Stir in Meyer lemon zest and cardamon.
Spray two 8x4 or 8.5x4.5 inch loaf pans with non stick cooking spray. On a lightly floured surface, roll out half the dough into a long rectangle about ¼ inch thick and about 8-9 inches along the short side of the rectangle. Spread half the white chocolate mixture over the top in an even layer, leaving a small ¼ inch border. Starting on the short side, roll up dough into a tight roll. Using a large sharp knife, cut the dough roll in half lengthwise. Turn the cut edges upward to two halves are next to each other with cut edges exposed on top. Twist the two halves together, pinching then tucking the end ends under the loaf. This process will be a bit slippery and messy from the white chocolate filling. Do the best to get an even twist, it will bake up nicely even if it looks a bit messy during the forming process. Place in prepared loaf pan, then repeat with other half of dough.
Cover loaf pans with plastic wrap and place in a warm, draft-free spot. Allow to rise until nearly doubled in size, about 1 hour.
Preheat oven to 350 degrees F. Bake babka for about 32-37 minutes, until top is golden and dough is cooked through. Remove from oven and let cool.
In a small bowl, make the glaze by stirring together powdered sugar, lemon juice, and salt. Adjust sugar or lemon juice amount to get a nice glaze consistency. It should be pourable but still a little thick. Once babkas are mostly cooled (still slightly warm to the touch), remove from loaf pans and drizzle glaze over the top. Allow to cool completely and glaze to set, then slice and serve.
Recipe by Wright Family Table at https://www.wrightfamilytable.com/meyer-lemon-white-chocolate-babka/