Bring a pot of salted water to a boil.
Slice the paneer into 1/2 inch thick slices and season both sides generously with salt and pepper.
Add the tagliatelle to the boiling water and cook until al dente, about 8 minutes.
While the pasta cooks, heat one tablespoon of olive oil over medium high heat in a sauté pan. Sear the paneer slices until browned on each side, about 2 minutes per side.
Set the seared paneer aside. In the same pan, over medium heat, melt the butter and add the capers and zest from half the lemon. Allow the picatta sauce to simmer together, 2 minutes.
When the pasta is cooked, using tongs, lift it directly from the boiling water into the pan with the picatta sauce (the extra pasta water will help emulsify the sauce).
Stirring constantly, heat the sauce and pasta until well combined. Top with the seared paneer.
Serve, drizzling any extra sauce over each serving, with lemon wedges for squeezing.