Pat the emu fillets dry with paper towels. Season both sides generously with salt and freshly ground black pepper.
Heat the olive oil and 20g of the butter in a skillet over medium-high heat. Sear the emu fillets for 3-4 minutes per side, until a golden-brown crust forms. Remove from the skillet, tent with foil, and let rest.
In the same skillet, melt the remaining butter. Add the coarsely crushed black peppercorns and stir to release their aroma.
Pour in the beef stock and simmer until reduced by half. Stir in the heavy cream and simmer over low heat until the sauce thickens slightly.
Return the emu fillets to the skillet and spoon the pepper sauce over them, allowing the flavors to meld.
Serve the fillets with the pepper sauce, alongside fresh vegetables or mashed potatoes. Garnish with fresh thyme sprigs.
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