Place a large saucepan over medium heat.
Add half-and-half, clam juice and white wine. Stir to mix.
Place another saucepan over medium heat.
Add 3 tablespoons.
When butter has melted and is hot (do not burn), add shallots. Sauté until translucent.
Add flour to butter mixture, stirring until flour is absorbed. Cook, stirring constantly, 2 - 3 minutes.
Add heated half-and-half mixture all at once to the shallot mix, stirring constantly with a wire whip to remove any lumps.
Add spinach, artichokes, shrimp, cayenne and black pepper. Bring to a boil.
Reduce heat. Simmer 3 minutes, stirring occasionally, so the mixture does not scorch.
Remove mixture from heat. Stir in cheese.
Pour dip into an oven proof bowl. Set aside and keep warm.
Turn on broiler.
Place a small saucepan over medium heat.
Add 2 tablespoons Butter. Cook until butter has browned but has not burnt.
Remove from heat. Set aside briefly.
Sprinkle Mizithra cheese over top of prepared dip.
Place dip bowl on a cookie sheet and place under broiler. Cook, watching closely, until cheese has just started to brown. Remove from oven.
Drizzle prepared brown butter over top.
Serve immediately, hot.