Preheat oven to 350°F and butter and flour a 9-inch springform pan.
For the strawberry ribbon, combine sliced strawberries, sugar, lemon zest, and lemon juice in a medium heavy saucepan.
Bring to a rapid boil over medium heat and cook for 15-20 minutes, stirring frequently, until strawberries are broken down and mixture is the consistency of preserves and coats the back of a spoon.
Remove from the heat and pour into a glass jar. Let cool to room temperature before using.
For the crumble topping, whisk together flour, sugar, brown sugar, cinnamon, and salt in a medium bowl.
Add melted butter and mix in with a fork until completely incorporated and mixture is crumbly. Stir in pecans. Chill until ready to use.
For the cake, whisk together flour, baking powder, baking soda, and salt in a medium bowl.
Beat butter, sugar, and vanilla in a separate large mixer bowl at medium speed until light and fluffy.
Add eggs and yolk one at a time and beat well.
Combine Greek yogurt and buttermilk in a small bowl.
Reduce speed to low and add flour mixture in three additions, alternating with yogurt mixture (begin and end with flour mixture).
Spoon half the batter into prepared pan and smooth with an offset spatula. Tap pan sharply to even out the batter.
Drop spoonfuls of strawberry sauce over the batter.
Spoon remaining batter into the pan and carefully smooth into an even layer. Tap pan sharply to reduce air bubbles.
Drop spoonfuls of strawberry sauce over the top of the batter and sprinkle evenly with chilled crumble.
Bake for 45 minutes, then tent with foil to prevent over-browning.
Continue baking another 20 to 30 minutes (for a total of 65 to 75 minutes) or until topping is golden, cake springs back to the touch and a tester emerges with a few crumbs attached.
Transfer to a wire rack and let cool for 20 minutes before removing sides from pan; cool for at least 1 hour before serving.
For the glaze, whisk together melted butter, salt, vanilla, powdered sugar, and milk in a small bowl. Drizzle glaze over coffee cake and let set before serving with fresh strawberries.
Store baked coffee cake at room temperature for up to 2 days, or wrap well and refrigerate. Reheat coffee cake in a warm oven (300°F) before serving.
Notes
Make ahead: Strawberry ribbon and crumble topping can be made 1-2 days in advance and refrigerated until ready to use.