Here are a couple of recipes from an online search that I did a several years ago when an aunt was wishing for butter roll like her father used to make.
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Grandmother's Old Fashioned Butter Roll

If you like butter, you'll love these simple but delicious butter rolls.

They're baked in a sweet milk sauce. Just the thing for a cold morning.
Prep Time: approx. 30 Minutes. Cook Time: approx. 40 Minutes. Original
recipe makes 12 rolls ( 12 servings). Recipe has been scaled to make 12
servings.

Printed from Allrecipes, Submitted by Donna Young

2 cups all-purpose flour
1/2 teaspoon salt
1 cup shortening
1/2 cup water
3/4 cup butter, softened
1/4 cup white sugar
1/2 teaspoon ground nutmeg
2 cups milk
2/3 cup white sugar
1 teaspoon vanilla extract

Directions

1. Preheat oven to 350 degrees F (175 degrees C). Lightly grease a 7x11 inch baking pan.

2. In a large bowl, mix together flour and salt. Cut shortening in thoroughly with a pastry blender until mixture resembles breadcrumbs. Stir in water and press dough together with your hands. Roll out pastry into a large rectangle. Spread the butter evenly over the pastry, then sprinkle on 1/4 cup sugar and nutmeg. Roll up the dough jelly roll style and pinch to seal. Cut into 12 even slices. Place the rolls in the prepared pan.

3. In a small saucepan, heat milk, 2/3 cup sugar and vanilla until mixture begins to bubble. Pour milk mixture over rolls.

4. Bake in preheated oven until brown, about 30 to 40 minutes.
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Butter Rolls
Categories: Gram
Yield: 1 Dozen

1/4 c Lukewarm water
1 pk Yeast
3/4 c Milk
1/2 ts Salt
3 tb Shortening
3 tb Sugar
1 Egg; beaten
3 c Flour
3 tb Melted butter

Dissolve yeast in water. Meanwhile, warm the milk
in a small saucepan, being careful not to boil. In
large bowl, mix salt, shortening, sugar, and
heated milk, and egg. Gradually add flour a cup at
a time.

Knead, let raise in greased bowl for about 1 1/2
hrs, punch down and let raise 5 min.

Divide into 12 equal parts. Form rolls in greased
muffin pans. Let rise again for 1 hr. Brush tops
of rolls with butter.

Bake 15 min at 400°. Remove from muffin tin and
brush tops and bottoms of rolls with butter.

This was my grandmother's recipe. When I was
twelve and stayed with her after Grandpa died, she
showed me how to make them. She used no recipe,
but I measured and wrote it down when we made
them. I still have the beat up card with my
mispellings and penciled recipe. Those visits were
a very special gift.

Charlotte Welch, October 1994.
Reformatted by Carolyn Shaw 1996