Combine the softened butter and cream cheese in the bowl of a standing electric mixer fitted with a paddle attachment. Cream together on low speed for about 2 minutes, until smooth and creamy.

Continue mixing on low speed and gradually add the flour, sugar, and salt. Mix for 2 more minutes. Be careful here while the mixer is in motion!

Turn the mixer off and remove the dough mixture from the bowl, wrap with plastic wrap and refrigerate until thoroughly chilled, 2 to 3 hours. (This dough can be made a day ahead.)

In a small mixing bowl, combine the apricot fruit spread and the walnuts. Set aside.

When the dough has chilled, divide into 4 equal portions. You will only work with one portion at a time, so keep the rest in the refrigerator until ready to use.

Position rack in bottom third of oven and preheat the oven to 350°F.

On a floured surface, use a floured rolling pin to roll one part of the dough into a circle, about 1/8 inch thick. Using a pizza cutter, trim the outer edges to form a smooth edge to the circle.

Using a spatula or the back of a spoon, spread one-fourth of the apricot filling onto the circle all the way to the edges. (You should have just enough for a thin layer of filling; it shouldn't be a thick coating.)

Using a small paring knife or a pizza wheel, cut the dough circle into 8 equal triangles.

Roll up each triangle, starting with the wide end and ending with the pointed end.

Place the rugelach pointed ends down on a parchment-lined baking sheet. (It's important to line the baking sheet or any oozing apricot filling will stick to the pan while baking.) Sprinkle a few teaspoons of coarse sugar on the tops of the rugelach. Repeat with the remaining dough portions and filling.  Chill before baking.

Bake for 12 minutes. Using oven mitts or pot holders, carefully open the oven and turn the pan 180 degrees. Continue baking for 13 to 16 more minutes, until golden brown.

Using oven mitts or pot holders, carefully remove the rugelach from the oven and cool completely on the baking sheet before serving.