Press the garlic clove. Heat a pan over medium-high heat, add the chicken hearts, and brown for 3-4 minutes per side. Add the pressed garlic and cook for 1 minute. Deglaze with the white wine, then add the chicken broth and some thyme. Reduce heat to low and simmer for 75 minutes.
Stir in the cream and some lemon juice. Grind the pimento, salt, and pepper together and stir into the pan. Simmer for 2 minutes.
Cook the spaetzle according to package directions (typically 3-5 minutes until tender).
Taste the chicken hearts and adjust seasoning with salt and pepper as needed.