Allow mahi mahi fillets to reach room temperature for 15-20 minutes. Pat dry with paper towels and season generously with salt and pepper.

Heat a skillet over medium-high heat with olive oil and butter. Cook fillets for 4 minutes on one side until golden brown, then flip and cook for 2-4 minutes until internal temperature reaches 137°F.

In the same skillet, reduce heat to medium and sauté shallots and garlic for 1-2 minutes until fragrant. Add chicken broth, thyme, and lemon juice, and bring to a simmer.

Stir in heavy cream and cornstarch mixed with cold water, simmer for 2-3 minutes until thickened; adjust seasoning.

Return cooked mahi mahi to skillet, coat in sauce, and serve hot garnished with parsley.