Bring a large pot of salted water to a boil. Prepare the chard: tear the leaves off the stems, separating the leaves and stems. Thinly slice the stems, then coarsely tear the leaves into bite-size pieces. Set both aside in separate bowls.
Prepare the leeks: trim off the bottom, and the dark green portions at the top. Halve the remaining white and pale-green portions lengthwise, then thinly slice them crosswise. Wash and drain. Set aside.
Prepare the bread crumbs: In a large skillet, melt 2 Tablespoons butter over medium heat. Add the bread crumbs, season lightly with salt, generously with pepper, and cook, stirring occasionally, until golden and toasted- 3 to 4 minutes. Transfer to a paper towel-lined plate.
Wipe out the skillet. Add the remaining 3 Tablespoons of butter and melt over medium-high heat. Add the leeks, chard stems, garlic, and thyme. Season with salt and pepper, and cook, stirring occasionally, until leeks start to wilt and soften- about 5 minutes. Add the torn chard, season with salt and pepper, and cook, stirring, until just wilted- about 2 minutes
Add the stock and heavy cream, and boil over high until thickened- about 10 minutes
Once the mixture is simmering, add the pasta to the pot of boiling water, and cook until al dente. Drain pasta.
Transfer the chard mixture to the empty pasta pot. Stir in the cooked, drained pasta, then sprinkle with the Parmesan, stirring vigorously to melt it into the sauce. Season to taste with salt and pepper.
Divide among shallow bowls or plates. Sprinkle generously with the prepared bread crumbs. Top with tarragon, and grate fresh lemon zest on top if using. Serve immediately.