Red Velvet Cinnamon Rolls

Prepare the Dough: Stir together warm water, yeast, and 1 teaspoon of the granulated sugar in a small cup or bowl; let stand 5 minutes.

Beat butter with a stand mixer fitted with a paddle attachment on medium speed until creamy, about 30 seconds. Gradually add remaining 1/2 cup granulated sugar; beat until light and fluffy, about 2 minutes. Add eggs, milk, lemon juice, and yeast mixture; beat until combined, about 1 minute. Whisk together cocoa, salt, and 4 1/4 cups of the flour in a medium bowl. Reduce mixer speed to low. Gradually add 1 cup cocoa mixture to butter mixture, beating until combined, about 30 seconds. Add food coloring gel; beat until just blended, about 30 seconds. Gradually add remaining cocoa mixture, beating until well combined, 2 to 3 minutes.

Sprinkle 1/4 cup of the flour onto a work surface. Turn dough out onto flour; knead until smooth and elastic, about 5 minutes, adding remaining 1/4 cup flour to dough and working all flour into dough as you knead. Place dough in a large bowl lightly coated with cooking spray, turning dough to grease top. Cover bowl; let dough rise in a warm, draft-free place until doubled in size, 1 1/2 to 2 hours.

Punch dough down in bowl. Turn out onto a lightly floured work surface. Roll into a 16- x 12-inch rectangle.

Prepare the Filling: Spread dough rectangle with very soft butter, leaving a 1-inch border. Stir together granulated sugar, brown sugar, and cinnamon in a small bowl; sprinkle evenly over butter. Sprinkle evenly with pecans. Roll up dough, jelly-roll style, starting at 1 long side. Trim and discard 1/2 inch on each end of dough log (your remaining log should be about 15 inches long). Cut log into 15 (1-inch) rolls.

Arrange rolls, cut side down, in a 13- x 9-inch baking pan lightly coated with cooking spray (5 rolls lengthwise by 3 rolls crosswise). Cover and let rise in a warm, draft-free place until doubled in size, 1 to 1 1/2 hours.

Preheat oven to 350°F. Uncover rolls. Bake in preheated oven until browned and slightly firm to the touch in center, 25 to 30 minutes. Let cool in pan 5 minutes.

Prepare the Cream Cheese Icing: Beat cream cheese and butter with an electric mixer on medium speed until creamy, about 1 minute. Reduce mixer speed to low; gradually add powdered sugar 1/2 cup at a time, beating until combined, about 2 minutes. Beat in vanilla and 1 tablespoon of the milk. Add remaining 1 tablespoon milk 1 teaspoon at a time, beating until icing is smooth and creamy. Brush over rolls. Serve warm.