Remove stamens from flowers, trying not to tear the delicate petals.
Fill a large, heavy saucepan with about 1-inch of vegetable oil. Set over medium heat and let it come up to desired temperature of 350 degrees.
In a bowl, combine goat cheese, cream, honey, and salt and pepper until smooth. Transfer to a piping bag or a zip-top bag with 1/2″ of the end cut off. Carefully insert tip of bag into a flower and fill with cheese mixture. Gently twist tops of petals to seal.
In a bowl, combine flour and beer and whisk until smooth. Using the stem as a handle, dip flowers into batter and flip to coat.
Gently lay battered flowers into hot oil. Repeat with another flower, battering and frying about 4 flowers at a time so as not to overcrowd the pan.
Fry flowers for 30 to 45 seconds, then flip and fry for another 30 to 45 seconds until light golden brown. Transfer to a wire rack or paper-towel lined plate. Repeat with remaining flowers. Serve warm.