Soak the sun dried tomatoes in a small cup of hot water for 30 minutes. Remove from the water and roughly chop.
Place tomatoes and lemon juice a bit at a time in a food processor with the goat cheese, pulsing until well blended and the flavor is satisfactory to you.
Combine the flour with a few good shakes of salt and pepper and blend well.
Pour out some of the flour mixture onto a clean dry plate.
Gently rinse and dry the zucchini blossoms, removing the stamens and pistils carefully (You may find that using tweezers helps, otherwise just be patient).
Spread petals slightly and spoon a small amount of filling mixture into each blossom, or squeeze from a plastic bag with a corner snipped off if it is easier for you to fill it that way.
Leave enough room at the top of each blossom to twist it closed.
Once blossoms are filled and sealed, dip each flower into beaten egg and roll gently in the flour mixture until lightly coated (If you find you’ve made too much filling, just save it to toss with pasta or spread on bread or crackers).
Add a couple of tablespoons of olive oil to a large pan to heat (medium high).
When the oil is hot enough, carefully place blossoms in the oil a few at a time with a slotted spoon, turning until each is golden and just lightly crispy.