Rinse the rice and the urad dal in a mesh strainer; place in a bowl and add fenugreek seeds. Cover with water; soak for 2 to 4 hours. Drain, reserving the soaking water.
Grind rice and urad dal in a blender, using enough reserved soaking water to reach the consistency of cake batter. Mix in salt; cover and place in a warm spot until batter is risen and fermented, 6 to 8 hours.
Stir fermented batter gently. Heat 1 teaspoon oil on a griddle over medium heat; wipe quickly with a wet cloth to diffuse heat.
Spread a large ladleful of batter quickly, thinly, and evenly over the griddle using the back of the ladle. Increase heat to high. Spread 2 teaspoons of oil on the surface of the dosa and cover with a lid; cook until top is spongy, 1 to 2 minutes. Remove lid; cook until bottom is crispy, about 1 minute more. Spread 1 teaspoon of butter on top of the dosa; transfer to a plate. Wipe griddle with a wet cloth and repeat with remaining batter.
