In the bowl of a stand mixer fitted with the paddle attachment, combine ½ cup warm water and yeast. Let stand until mixture is foamy, about 10 minutes.
In a medium saucepan, heat sour cream, butter, sugar, and salt over medium-low heat, stirring constantly, until butter is melted, 3 to 4 minutes. Let cool to 1100F, about 10 minutes. Beat in eggs. Add sour cream mixture to yeast mixture, beating until combined.
Add flour, 1½ cups cheese, garlic, and thyme, and beat at medium speed until well combined. Spray a large bowl with cooking spray. Place dough in bowl, turning to grease top. Cover and let rise in a warm, draft-free place (75°F) until doubled in size, 1 to 1½ hours.
Spray 2 (12-cup) muffin pans with cooking spray.
Divide dough into 24 equal portions. Working with 1 portion at a time (keep remaining dough covered to keep from drying out), divide each portion into 3 pieces; roll each piece into a ball. Place 3 dough balls in each prepared muffin cup. Cover and let rise in a warm, draft-free place (75°F) until doubled in size, about 30 minutes.
Preheat oven to 350°F. Bake until golden brown, 15 to 18 minutes. Remove from oven. Brush with melted butter, and sprinkle with remaining ¼ cup cheese. Garnish with thyme, if desired.
Recipe by Bake from Scratch at https://staging.bakefromscratch.com/sour-cream-rolls/