Adjust oven rack to upper-middle and lower-middle positions and heat oven to 200ºF (93ºC). Once oven comes up to temperature, turn oven off. Lightly grease a large bowl with nonstick spray. Line 2 baking sheets with parchment paper.

Mix flour, yeast, and salt in bowl of stand mixer fitted with dough hook.

Whisk together 1 ⅓ cups milk, melted butter, honey, yolks, and 2 teaspoons vanilla in large measuring cup.

Turn mixer to low speed and slowly add milk mixture. Once dough comes together, increase speed to medium and mix until dough is shiny and smooth, about 6 minutes. (Dough will be sticky.)

Turn dough onto heavily floured work surface, shape into a ball, and transfer to greased bowl. Cover bowl with plastic wrap or a clean kitchen towel and place in turned-off oven, with door open, until dough is nearly doubled in size, about 20 minutes.

Meanwhile, for the filling, add almond paste, jam, and 4 ounces cream cheese to a stand mixer fitted with paddle attachment. Mix on medium speed until smooth, about 2 minutes. Add diced apricots and mix on low just to combine, about 10 seconds. Cover with plastic and refrigerate until ready to use.

On lightly floured surface, divide dough into 2 equal pieces. Working with 1 piece of dough at a time, roll dough into 18✕9-inch rectangle; long side facing you.

Repeat with remaining dough and filling.

Trim ½-inch of dough off ends of roll, then form each roll into ring.

Gently rotate each section of dough cut side up (twist each section in same direction).

Cover with plastic wrap coated with cooking spray or clean kitchen towel; return to oven until rings have puffed slightly, 45–50 minutes. Remove from oven and heat oven to 375ºF (190ºC).

Whisk a reserved egg white in small bowl (reserve rest for another use), then brush rings with egg white. Bake until deep brown, 23–25 minutes, switching and rotating pans halfway through baking. Transfer sheets to wire rack and cool.

Meanwhile, whisk confectioners' sugar, remaining 2 ounces cream cheese, 1 tablespoon milk, ½ teaspoon vanilla, and salt in small bowl until smooth. Drizzle icing over baked coffee cakes and serve warm.