Preheat oven to 375˚F.
Cook sliced potatoes in boiling salted water for 5 minutes; drain under cold water and cool immediately. Set aside.
Heat olive oil in a skillet over medium heat and add onion; cook for 2 minutes.
Add ground beef; break apart with a wooden spoon and cook until browned, about 5 minutes.
Stir in garlic.
Add tomato paste and stir until completely incorporated.
Season beef with paprika, salt, and pepper. Taste for seasonings and adjust accordingly. Remove from heat and set aside.
Grease a 13x9-inch baking dish.
Layer 1/3 of the sliced potatoes on the bottom of the prepared baking dish.
Top the potatoes with half of the ground beef mixture.
Spread 1/3 potato slices over beef.
Add remaining beef mixture and top with last layer of potatoes. Set aside.
In a separate bowl, whisk the eggs; then whisk in the milk, salt, and pepper; continue to whisk until thoroughly combined.
Pour the milk mixture over the potatoes.
Bake for 45 to 55 minutes, or until custard is set and potatoes are a golden brown.
Let rest 10 minutes before cutting and serving.