In a sauté pan on high heat, heat 1 Tbs olive oil. When hot, add the sausage. Cook, stirring occasionally, until evenly browned, about 1 minute. Add the onions and carrots. Cook until the onions are slightly translucent, about 2 minutes. Add the garlic, continuously stirring to make sure it doesn't burn. Once translucent, after about 90 seconds, add the wine. Cook the wine until the pan is almost dry, 4 to 5 minutes. Add the chicken stock, bring to a simmer, and decrease the heat to low.
Drop the fresh Sabbiatos orecchiette into the boiling water. Once the pasta is cooked 80% through, until almost al dente, about 2 minutes, transfer to the sauté pan. Reserve the pasta water. Stir to incorporate the pasta and increase the heat to high.
Add the 2 tsps. extra-virgin olive oil to the simmering pan sauce and fold in the Padron peppers
Let the pasta finish cooking in the meat sauce. When the pasta is tender, add the butter to the pan and stir quickly to emulsify. Add the sherry vinegar and season with salt to taste. Remove from the heat.
Finish with freshly grated Parmigiano-Reggiano.
Notes
Credit for recipes goes to: Flour and Water pasta by Thomas McNaughton with Paolo Lucchesi