In a large skillet, heat oil over medium-high heat. Add frog legs, and lightly brown on both sides, about 10 minutes. Transfer frog legs to a platter, and set aside.
Add flour to skillet, and cook, stirring constantly, until a tan roux forms, 4 to 5 minutes.
Add onion, bell pepper, celery, garlic, salt, and cayenne to skillet; cook until wilted, 3 to 4 minutes.
Add tomato, stock, hot sauce, thyme, and bay leaf. When mixture begins to simmer, reduce heat to medium. Simmer, uncovered, until sauce reduces by a third, 25 to 30 minutes, stirring occasionally.
Lay frog legs in sauce, and cook for 8 to 10 minutes, basting with sauce. Taste, and adjust seasoning, if needed. Stir in parsley and lemon juice. Remove bay leaf, and serve over rice. Garnish with parsley, if desired.
Recipe by Louisiana Cookin' at https://louisianacookin.com/frog-leg-sauce-piquante/