Pour the cream into a shallow, wide container like a hotel pan. Pour the cream into the pan and cover with several layers of plastic wrap. Cut a small hole in the plastic to insert your smoking gun hose. Cold smoke the cream for 15 minutes making sure to light the bowl of your smoking gun periodically. Remove the hose and cover the whole to allow to steam in the cold smoke for another 15 minutes.
Melt butter in a medium sauté pan over medium heat. After a minute, add garlic, cold-smoked cream, potatoes, salt, and ground white pepper. Cover and simmer on the stove for 20 minutes over medium low until the potatoes have cooked and are soft enough to pierce with a fork. Remove the garlic cloves. Set aside to cool.
In a food processor, add your flour and salt. While the food processor is running, slowly add in the whole eggs, egg yolks, and olive oil. When combined, the dough should feel sandy to the touch but still stick to itself when pressed between your fingers. Dump the contents of the food processor onto a clean work surface and need until it forms a smooth ball. Cover in plastic wrap and allow to rest for 30 minutes.
Roll the pasta into a sheet that is the thickness of 6 Post-It notes (a trick I learned in cooking school via Evan Funke). Fold into thirds and slice into thick noodles, approximately 1/2-inch wide.
Prepare a cooking station. You’ll need space for a pot of water and a non-stick pan to cook and plate four separate servings. Bring the pot of water to a boil with a handful of kosher salt. Cook the pasta in batches for one minute. Using a spider, transfer the cooked pasta to the non-stick pan warmed over medium high heat with 1/2 cup of your smoked potato cream sauce. Toss the pasta with a ladle full of pasta water. While the pasta is finishing in the sauce, start to cook your next batch of pasta. Repeat the same process until all four portions are complete. Top each with a generous spoonful of caviar and a pinch of chives. Enjoy!