Combine warm milk, yeast, and 1 tbsp sugar. Let sit 5–10 minutes until foamy.
Add eggs, remaining sugar, melted butter, vanilla, flour, and salt. Knead until dough is smooth.
Let rise in a greased bowl until doubled, about 1 hour.
Mix lemon filling ingredients into a spreadable paste.
Roll dough into a rectangle. Spread with lemon filling. Roll up and cut into 12 rolls.
Place rolls in a greased 9x13 pan. Let rise again for 30–45 minutes.
Bake at 350°F (175°C) for 23–28 minutes or until lightly golden.
Beat frosting ingredients until smooth and creamy.
Frost warm rolls and serve.