Blend the flour and squid ink in a food processor for at least 5 minutes (this helps bring out the intense black color of the squid ink). Add the olive oil, eggs and some salt and continue to mix until it forms a ball. Transfer to a lightly-floured surface and knead by hand for 5 minutes. Wrap the pasta dough tightly in plastic wrap and let it rest for at least 1 hour (2 hours is preferable). Once rested, roll out to desired thickness using a pasta roller, then cut to linguine size. Lay the pasta on a baking sheet that has been lightly dusted with flour.
For the oysters:
Meanwhile, soak the oysters in the buttermilk in the refrigerator for at least 1 hour and up to 12 hours.
For the balsamic reduction:
Pour the vinegar into a saute pan or small saucepan and bring to a simmer. Simmer until reduced by half and thick enough to coat the back of a spoon, 45 minutes.
For the hollandaise:
Heat the butter in a small saucepot until melted and slightly simmering. Combine the lemon juice, egg yolks, hot sauce and some mustard and salt in a small food processor. Turn the food processor on, and slowly drizzle in the butter until emulsified. Store in a warm place until needed, or store in a gallon-size resealable plastic bag and refrigerate.
For the basil oil:
Bring a medium pot of lightly salted water to a boil. Prepare a bowl of ice water. Once water is at a full boil, drop in the basil and count to 10. Drain the basil and quickly plunge into the ice water. Let sit for a minute or so, and then place the basil into a kitchen towel and firmly squeeze out any excess water. Transfer the basil to a blender with the oil and blend on high for 1 full minute. Strain through a cheesecloth to catch all the pulp, leaving you with only the basil-infused oil. Keep cold; it will last in the refrigerator for up to 4 days.
For cooking and plating:
Heat the oil in a 2-quart stock pot to 350 degrees F. Bring a pot of lightly salted water to a boil. Cook 1 serving of pasta for 2 to 3 minutes, then plunge into the ice water to "shock". Once cold, drain and dress lightly with olive oil.
Fry the pancetta until nicely browned in a heated saute pan. Add the chard and cook until lightly wilted. Add the pasta and cook to warm through, adding more salt and pepper to taste and the chicken stock to add moisture.
Remove the oysters from the buttermilk and lightly dredge in seasoned flour. Tap off excess flour and lightly fry the oysters until golden brown. Transfer to paper towels to drain.
Gently "twirl" a nest of pasta onto a plate using a fork, making sure to get the Swiss chard and a few pieces of pancetta. Place the fried oysters on top. Dollop on the mustard hollandaise using a soup spoon. Top with chopped chives and garnish with basil oil, micro greens and balsamic reduction.
The balsamic reduction can be made days ahead of time and stored in the refrigerator for 1 to 2 weeks.
Use remaining pasta, hollandaise, balsamic reduction and basil for additional servings. Add more fried oysters, Swiss chard and pancetta as needed.