Soak sweetbreads in a large bowl of water for 1 hour; drain.
Place sweetbreads in a saucepan and cover with cold water; bring to a boil. Drain. Run cold water over sweetbreads to cool.
Return sweetbreads to the saucepan and cover with cold water again. Add 1 tablespoon butter, lemon juice, and salt; bring to a boil. Simmer for 10 minutes. Remove from heat and let cool.
Melt 3 tablespoons butter in a heavy-bottomed skillet over medium heat. Add mushrooms; cook and stir until tender, about 5 minutes. Transfer to a plate.
Melt remaining 3 tablespoons butter in the skillet. Add flour; cook and stir until a paste forms, about 1 minute. Season with paprika and cayenne. Pour in milk slowly, whisking until sauce is smooth, 3 to 5 minutes.
Stir sweetbreads, mushrooms, and peas into the sauce; cook until peas are heated through, about 5 minutes. Season sweetbreads with salt. Serve garnished with jalapeno pepper.
I used frozen New Zealand lamb sweetbreads. These did not need black veins and skin removed, as may be necessary with fresh ones. Calf sweetbreads may also be used, but these will need more attention to prepare.
Per Serving: 375 calories;31.6 g fat;
4.8 g carbohydrates;
17.8 g protein;
326 mg cholesterol;
242 mg sodium.