Heat oil in a large heavy-bottomed saucepan over medium heat. Add onions and garlic, and cook, stirring often, until tender and translucent, about 5 minutes. Add tomato paste and cook, stirring often, until oil is vividly orange, 10 minutes.

Add tomatoes and break into chunks. Reduce heat to a simmer, and cook, stirring every 10 minutes or so, until sauce is thickened and reduced by about half, 1 1/2 to 2 hours.

Remove from heat, stir in oregano. Taste and season with salt and pepper as needed. Let stand until cooled, about an hour.

In a large bowl, whisk together ricotta cheese and eggs. Add parsley and stir to mix. Taste and season with salt and pepper.

Preheat oven to 350°F.

For assembly, roll pasta into very thin sheets as needed.

Spread about 1 cup sauce on bottom of an 8x8-inch pan. Place a layer of pasta sheets over the sauce, covering it completely. Add a layer using half of the ricotta mixture, followed by another layer of pasta sheets. Spread sauce, reserving about 1 cup, over the pasta, then another layer of pasta, followed by the remaining ricotta mixture. Finish with a layer of pasta and the remaining tomato sauce.

In a small bowl, toss the mozzarella cheese with a small amount of salt and pepper, then spread on top of the lasagna.

Place in oven and bake, uncovered, until bubbly and browned in spots.

Remove from oven and let stand about 15 minutes before serving.