Put all ingredients, except oil, in bowl (if hand whisking) or food processor. While mixing slowly drizzle in oils until smooth and emulsified.
Toss all ingredients in a bowl with 3-4 tablespoons dressing. Salt & pepper to taste.
For the sweetbreads:
Heat Oven to 400 Degrees. Heat large heavy sauté pan. Season pressed sweetbread with salt and pepper, dredge in flour.
Heat heavy sauté pan, add oil and 2 tablespoons butter, warm until butter melts. Add floured sweetbread, sear well on all sides – three minutes on each side – add remaining butter, rosemary and thyme – baste sweetbreads until firm – approximately four minutes. Remove to plate and keep warm.
Add garlic and shallot to the same pan with residual butter. Add mushrooms and stir until brown. Deglaze pan with wine, add heavy cream and simmer until reduced by half.
Divide sauce among four plates, slice sweetbreads, set on sauce and garnish with carrot salad.