Preheat the oven to 425F/218C. Line one or two large baking sheets with parchment paper or silicon mats. Prepare a large pastry bag with a French star tip such as 8FT.
Prepare the pate a choux dough first. Sift the flour into a large bowl and set aside. Into a small saucepan, add the butter, salt and water. Cook the mixture over medium-high heat until the butter is melted and comes to a simmer. Add the flour all at once and stir until the a dough ball forms, about 1 minute.
Transfer the dough into a large mixing bowl and allow it cool until warm to touch, about 15 to 20 minutes. Once cooled, begin adding the eggs, one at a time. Use a hand-mixer or whisk to mix the egg into the dough after each addition. Transfer the dough into the prepared pastry bag, packing the dough into the bag without air pockets.
Pipe 4 to 6-inch long eclairs onto the prepared parchment paper or silicone, spacing about an inch apart. Bake the eclairs in the preheated oven at 425F/218C for 10 minutes, then reduce oven temperature to 375F/190C and bake for an additional 35 to 40 minutes, until the eclairs are a deep golden brown. Avoid opening the oven door during baking - cold air will cause the eclairs to fall flat. Once they are baked, cool them completely on a wire rack.
Prepare the basil filling. Place the basil leaves and confectioner's sugar into a food processor and pulse for about a minute until a smooth paste forms. Transfer the basil paste into a bowl with the softened cream cheese and white chocolate. Beat the ingredients together for a few minutes on high speed until smooth.
In a separate bowl, whisk the chilled heavy cream for about 4 minutes on medium-high speed until medium peaks form. Add the basil and cream cheese mixture to the whipped cream and whisk again for about 1 minute, until stiff peaks form.
To fill the eclairs, first use a filling tip, such as Wilton #230 to punch 3 small, evenly spaced holes into the bottom of each eclair. Transfer the filling into a pastry bag and pipe each eclair full of cream.
Next, prepare the ganache. Combine the cream and white chocolate in a wide bowl. Heat in the microwave for about 1 1/2 minutes, stirring every 30 seconds, until the chocolate is melted and smooth. Allow the ganache to cool for about 10 minutes, until slightly thickened. Add the strawberry extract and a few drops of red food coloring and mix well. Dip each eclair into the ganache and let any excess glaze drip off before placing onto a cooling rack.
Once eclairs are filled, keep them refrigerated single layer on a tray. When ready to serve, garnish with sliced strawberries and fresh mint or basil leaves. Eclairs will stay good for 3 days in the fridge.