Roast the tomatoes: Preheat the oven to 400°F. Add the chopped tomatoes to a small quarter-sheet pan along with the olive oil, dried oregano, garlic cloves, and salt. Toss well and spread into an even layer. Roast for 25–30 minutes, until the tomatoes are soft, caramelized, and jammy.
Mash the tomatoes: Once roasted, squeeze the garlic out of its skins and mash it into the tomatoes to form a rustic, sticky tomato-garlic paste. Set aside.
Sauté aromatics: In a large pot or Dutch oven, heat a drizzle of olive oil over medium heat. Add the bacon and cook until browned and the fat has rendered. Remove the bacon with a slotted spoon and set aside, leaving the fat in the pot. Add the onion and cook for 5 minutes, seasoning lightly with a pinch of salt. Add the carrots and celery with another pinch of salt and cook 5 minutes. Continue cooking until the vegetables begin to soften. Stir in the mushrooms and sauté for about 2 minutes, just until they release a bit of moisture. Add the minced garlic, dried thyme and crushed red pepper flakes and let everything steam gently for about 1 minute, without browning.
Add lentils and tomato paste: Add the lentils to the pot along with the roasted tomato-garlic paste. Stir well and let this mixture sauté for 1 minute, coating the lentils and slightly caramelizing the paste.
Add liquids: Deglaze the pot with the white wine, scraping up any browned bits from the bottom. Let the wine reduce slightly, about 1–2 minutes. Add the chicken broth and bay leaves. Bring to a gentle simmer, cover partially, and cook for 25–35 minutes, until the lentils are tender.
Season the soup with salt, black pepper, smoked paprika, lemon zest and lemon juice. Taste and adjust seasoning as needed. Stir in the reserved bacon and the Swiss chard, adding the stems first, then the leaves. Simmer just until the chard is tender and wilted, about 1 minute.
Serve: Remove the bay leaves and serve with grated Parmesan and a generous drizzle of olive oil.