Heat olive oil in a saucepan over medium heat. Add shallots and cook until soft and translucent, about 5 minutes. Add peas and cook another 5 minutes. Add broth and bring to a low boil. Reduce heat and simmer until peas are just tender (not mushy), about 15 minutes.
While peas are simmering, cook bacon on a skillet until crisp. Once crisp, drain on paper towels and cut each strip in half widthwise and set aside.
Puree the peas and broth mixture until smooth, using either a handheld immersion blender or standing blender. (Use caution pureeing hot liquids.) Once mixture is smooth, return the soup to the pot over low heat.
Stir in the yogurt and lemon juice and heat through. Add salt and pepper (add more to taste if necessary).
Serve warm or chilled in shot glasses. Sprinkle with smoked paprika. Top each with a swirl of herbed olive oil. Cut small sliver in radish slices and place one on side of each glass along with a halved slice of bacon for garnish.