First add the butter, ½ cup of the sugar, and the dried strawberry pieces to a mixing bowl and cream together until light and fluffy, about 1-2 minutes. Then, add in the flax egg and vanilla bean paste/extract and whip together about 30 more seconds to combine.
Next, add in sifted flour, baking powder, baking soda, and salt to the mixing bowl. Mix until a thick, yet slightly sticky, cookie batter forms. Do not overmix or else you will form too much gluten and the cookies will not spread as much and will be tough.
Cover the mixing bowl of dough with plastic wrap or a similar material and add to the fridge to chill for 30 minutes- 1 hour.
Line a baking sheet in parchment paper and preheat the oven to 350F. Next, remove the dough from the fridge and use a 2 Tbsp cookie scoop to form your cookie dough (about 45 grams of dough per cookie). Roll into balls between your palms and then roll in the 2 Tbsp of sugar that was set aside so that each dough ball is coated in sugar.
Place the strawberry cookie dough balls onto the baking sheet. Then, slightly press each dough ball down with your palm. Make sure that each cookie is kept about 2 inches apart since they will spread slightly while baking.
Bake for 12-14 minutes until bottoms are lightly browned and the cookie is cooked, but still has soft centers. The cookies will continue baking after they are removed from the oven so the centers should be soft and slightly under-cooked, but not glossy or raw, when they are removed from the oven. Please be careful not to overcook these cookies as they will still be soft but will lose their "chewy" texture if overcooked.
Remove the cookie tray from the oven and immediately tap the tray on the counter to produce a more “wrinkly” cookie. Then, let the cookies cool on the baking sheet for 5 minutes.
Once the cookies have cooled, make the vanilla icing. Add the powdered sugar, vanilla paste/extract, and plant milk/water to a bowl and mix until a thick icing forms. The icing should be very thick or else it will not hold it's shape.
Drizzle the icing over the cookies with a spoon and then top each cookie with additional dried strawberry crumbles. Serve and enjoy!